# matrix algebra

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BSc/MSci/MSc EXAMINATION 2014 For internal students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

For internal students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

BSc/MSci/MSc EXAMINATION 2014 For internal students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

For internal students of Royal Holloway DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

DO NOT TURN OVER UNTIL TOLD TO BEGIN MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

MT1820: MATRIX ALGEBRA MT1820R: MATRIX ALGEBRA – PAPER FOR RESIT CANDIDATES Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R

Time Allowed: TWO hours All questions may be attempted but credit will only be given for the best four answers. A borderline first class mark would normally require answers to the equivalent of three complete questions. MT and Type A Calculators are permitted. °c Royal Holloway, University of London 2014 Page 1 of 4 2013–14 Important Copyright Notice This exam paper has been made available in electronic form strictly for the educational benefit of current Royal Holloway students on the course of study in question. No further copying, distribution or publication of this exam paper is permitted. By printing or downloading this exam paper, you are consenting to these restrictions. 2013–14 Page 2 of 4 MT1820 1. Let A, B, C, D be points in R 3 with position vectors a =   1 2 −2   , b =   2 1 4   , c =   −1 3 2   , d =   3 3 2   respectively. (a) Calculate a · b and (b − a) × (c − a). (b) Calculate the area of the triangle ABC. (c) Find an equation of the plane through A, B, C in the form v · n = d. (d) Do the position vectors of the points of the plane through A, B, and C form a subspace of R