Find the matrix X such that – A + 3B + X = 0, where [(-2,6)(5,8)] and B = [(1,2)(-2,3)]

Question

Find the matrix X such that – A + 3B + X = 0, where \(\begin{bmatrix}-2&6 \\[0.3em] 5 &8 \end{bmatrix}\) and B = \(\begin{bmatrix}1&2 \\[0.3em] -2 &3 \end{bmatrix}\)

Answer 1

Given , –A + 3B + X = 0 

⇒ X = A – 3B

⇒ X = \(\begin{bmatrix}-2&6 \\[0.3em] 5 &8 \end{bmatrix}\) -3\(\begin{bmatrix}1&2 \\[0.3em] -2 &3 \end{bmatrix}\)

= \(\begin{bmatrix}-2&6 \\[0.3em] 5 &8 \end{bmatrix}\) - \(\begin{bmatrix} 3 & 6 \\[0.3em] -6 & 9 \end{bmatrix}\) = \(\begin{bmatrix}-2-3 &6-6 \\[0.3em] 5-(-6)&8-9 \end{bmatrix}\) = \(\begin{bmatrix}-5&0 \\[0.3em] 11 &-1 \end{bmatrix}\)