2. (a) Consider the matrices A = B 2] [43] 73 3-2 84 (i) Use matrix arithmetic to calculate each of: AB, BA, A + B, AC + BC. (ii) Let Ct be the transpose of C. In each case determine the dimensions of the resulting matrix, or explain why the matrix does not exist: BC", Ct A, Ct (BC), (CC¹) A. (iii) Compute det (B) and det(B³). (b) Let = (1, -2,3), = (2,-1, 1) be vectors in 3-dimensions. (i) Calculate each of vow, |||| and ||w|. (ii) Find the orthogonal projection Pr(w) of w onto . (iii) Determine the cosine of the angle between 7 and w. (c) Find the equation of the plane that contains (2, 1,4), (-1,3, 2) and (4,-1,2).

2. (a) Consider the matrices A = B 2] [43] 73 3-2 84 (i) Use matrix arithmetic to calculate each of: AB, BA, A + B, AC + BC. (ii) Let Ct be the transpose of C. In each case determine the dimensions of the resulting matrix, or explain why the matrix does not exist: BC", Ct A, Ct (BC), (CC¹) A. (iii) Compute det (B) and det(B³). (b) Let = (1, -2,3), = (2,-1, 1) be vectors in 3-dimensions. (i) Calculate each of vow, |||| and ||w|. (ii) Find the orthogonal projection Pr(w) of w onto . (iii) Determine the cosine of the angle between 7 and w. (c) Find the equation of the plane that contains (2, 1,4), (-1,3, 2) and (4,-1,2).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 19EQ

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