#53 1:14ull ?Done elementary_linear_algebra_8th_...To JT2 -1]*1: J28. A -! 0-17 20 B-8 - 17Cede cn2.1 Exercises49Matrix Size In Exercises 29-36, let A, B, C, D, and FWriting a Linear Combination In Exercises 49-52,be matrices with the sizes shown below.write the column matrix b as a linear combination of theA: 3 x4 B: 3 x4 C: 4 x 2 D: 4 x 2 E: 4 x 3columns of A.[! -1If defined, determine the size of the matrix. If notdefined, explain why.49. A--341b =329. A + B30. C+E231. D32. -4450. A =-1233. AC34. BE35. E- 2436. 2D +C-5Solving a Matrix Equation In Exercises 37 and 38,solve the matrix equation Ax = 0.51. A - 0 -1. b[2-137. A = *--3 5)3 4– 22]52. A-432Solving a Matrix Equation In Exercises 53 and 54,solve for A.338. A-I -01 -12Solving a System of Linear Equations In Exercises39-48, write the system of linear equations in the formAx = b and solve this matrix equation for x.sa. ; - 139. -x, +x, 4-2x, + x, =040. 2x, + 3x, - 5X, + 4x, - 1042. -4x, + 9x, --13Solving a Matrix Equation In Exercises 55 and 56,solve the matrix equation for a, b, e, and d.41. -2r, - 3x, - -46x, + - 36X, - 3x, = 1243. X- 21, + 3x,- 9-x, + 3x, - x, --62x, - Sx, + 5x,- 1744. , + - 3x,- -IDiagonal Matrix In Exercises 57 and 58, find theproduct AA for the diagonal matrix. A square matrix-A + 2x3X - X + X, = 2X- 5x, + 2x,--20-3x, + X - X - 8-2, + Sx, - - 16... 0... 0a .. 0A- 0 045.0 ... ais a diagonal matrix when all entries that are not on themain diagonal are zero.46. x - + 4x, - 17K + 3x,-6x, + Sx, -47. 2x, - +--||[2 0 012 0 58. A - 0 -3-14057. А -33x, - X, - X,--3Finding Products of Diagonal Matrices In Exercises59 and 60, find the products AB and BA for the diagonalmatrices.+ ,- 3x, - -4X, +x, + 2r,48. X, +x,59. A - ; - -|X, +360. A-0 -530-7B =4X +-0-x, +x, - x, +x,- X= 512Cecnpe ped dy d i50Chapter 2 Matrices61. Guided Proof Prove that if A and R are diagonalmatrices (of the same size), then AB - BA.72. Show that no ? x ? matrices A and Rexist that satisfythe matrix equationAB - RA -Getting Started: To prove that the matrices AR and RAare equal, you need to show that their correspondingentries are equal.(i) Begin your proof by letting A- [a,] and 8- [b,be two diagonal nxn matrices.73. Exploration Let i- -i and letA - 1 and B- : 4(ii) The ijth entry of the product AB is(a) Find A. A'. and A. (Note: A - AA.A - AAA = APA, and so on.) Identify any similaritieswith P. P, and i.(ii) Evaluate the entries c, for the two cases i + j and(b) Find and identify B.

Name: #53 1:14ull ?Done elementary_linear_algebra_8th_...To JT2 -1]*1: J28.
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Description: #53 1:14ull ?Done elementary_linear_algebra_8th_...To JT2 -1]*1: J28. A -! 0-17 20 B-8 - 17Cede cn2.1 Exercises49Matrix Size In Exercises 29-36, let A, B, C, D, and FWriting a Linear Combination In Exercises 49-52,be matrices with the sizes shown bel