If p= ​​[(-3,1)(2,5)], Q = [(1,6)(-4,0)] and R [(4 , -1)(2, 3)] find the value of 4P - 2Q + 3R.

Question

If P = \(\begin{bmatrix} -3 & 1 \\[0.3em] 2 & 5\end{bmatrix},\) Q = \(\begin{bmatrix} 1 & 6 \\[0.3em] -4 & 0\end{bmatrix}\) and R =  \(\begin{bmatrix} 4 & -1 \\[0.3em] 2 & 3\end{bmatrix}\) find the value of 4P – 2Q + 3R.

Answer 1

4P - 2Q + 3R

= 4\(\begin{bmatrix}-3 & 1 \\[0.3em] 2&5\end{bmatrix}\) - 2\(\begin{bmatrix}1 & 6 \\[0.3em] -4 & 0 \end{bmatrix}\) + 3\(\begin{bmatrix}4 & -1 \\[0.3em] 2&3\end{bmatrix}\)

= \(\begin{bmatrix}-12 & 4 \\[0.3em] 8&20\end{bmatrix}\) - \(\begin{bmatrix}2 & 12 \\[0.3em] 8&0\end{bmatrix}\) + \(\begin{bmatrix}12 & -3 \\[0.3em] 6&9\end{bmatrix}\)

= \(\begin{bmatrix}-12-2+12 &4-12-3 \\[0.3em]8-(-8)+6&20-0+9\end{bmatrix}\) = \(\begin{bmatrix}-2 & -11 \\[0.3em] 22&29\end{bmatrix}\)