1. Attempt the following: (a) If A = [2 5; 0 1], B = [4 -1; 2 0], C = [1 7; 5 2], find 5A - 3B + 2C. (b) If A = [2 3 1; 0 -1 5], B = [1 2 -6; 0 -1 3], evaluate 3A - 4B. (c) Is the... 1. Attempt the following: (a) If A = [2 5; 0 1], B = [4 -1; 2 0], C = [1 7; 5 2], find 5A - 3B + 2C. (b) If A = [2 3 1; 0 -1 5], B = [1 2 -6; 0 -1 3], evaluate 3A - 4B. (c) Is the sum [1 -2 0; 4 1 3] + [0 -1 3] defined? Justify your answer. (d) If A = [1 2 3; 0 4 5; 7 8 9], B = [2 0 3; 4 0 -1; 2 3 0], evaluate 2A - 3B. (e) If A = [2 3; 4 7], B = [1 3; 4 6], find 2A + 3B - 4I, where I is the unit matrix of order two. (f) Find X, if [4 5; -3 6] + X = [10 -1; 0 -5]. (g) If A = [4 2 -5; -3 5 3], B = [3 5 -1; 1 2 5], find the matrix X such that A + X = B. (h) If A = [2 -1; 4 3], B = [-1 2; 4], find the matrix X such that 2A + X = 3B. Read more

Steps to Solve

1. Calculate (5A)
   Multiply matrix (A) by 5.
   Given (A = \begin{pmatrix} 2 & 5 \ 0 & 1 \end{pmatrix}),
   [ 5A = 5 \cdot \begin{pmatrix} 2 & 5 \ 0 & 1 \end{pmatrix} = \begin{pmatrix} 10 & 25 \ 0 & 5 \end{pmatrix} ]

2. Calculate (3B)
   Multiply matrix (B) by 3.
   Given (B = \begin{pmatrix} 4 & -1 \ 2 & 0 \end{pmatrix}),
   [ 3B = 3 \cdot \begin{pmatrix} 4 & -1 \ 2 & 0 \end{pmatrix} = \begin{pmatrix} 12 & -3 \ 6 & 0 \end{pmatrix} ]

3. Calculate (2C)
   Multiply matrix (C) by 2.
   Given (C = \begin{pmatrix} 1 & 7 \ 5 & 2 \end{pmatrix}),
   [ 2C = 2 \cdot \begin{pmatrix} 1 & 7 \ 5 & 2 \end{pmatrix} = \begin{pmatrix} 2 & 14 \ 10 & 4 \end{pmatrix} ]

4. Combine results: (5A - 3B + 2C)
   Perform the operation (5A - 3B + 2C).
   First, calculate (5A - 3B):
   [ 5A - 3B = \begin{pmatrix} 10 & 25 \ 0 & 5 \end{pmatrix} - \begin{pmatrix} 12 & -3 \ 6 & 0 \end{pmatrix} = \begin{pmatrix} 10 - 12 & 25 - (-3) \ 0 - 6 & 5 - 0 \end{pmatrix} = \begin{pmatrix} -2 & 28 \ -6 & 5 \end{pmatrix} ] Now add (2C):
   [ (-2, 28 \ -6, 5) + (2, 14 \ 10, 4) = \begin{pmatrix} -2 + 2 & 28 + 14 \ -6 + 10 & 5 + 4 \end{pmatrix} = \begin{pmatrix} 0 & 42 \ 4 & 9 \end{pmatrix} ]