Question

Solve the matrix multiplication ​

Answer 1

Since order is 2×3 and 3×2,

resultant matrix will have order 2×2.

a11=(-3×2+-1×1+3×3)=2

a12=(-3×-3+-1×0+3×1)=12

a21=(-1×2+0×1+2×3)=4

a22=(-1×-3+0×0+2×1)=5

Hence matrix:-

(2 12)

(4. 5)

Answer 2

$\underline{\underline{\huge{\mathbf{Question:}}}}$

$\bold{\left[\begin{array}{ccc}-3&-1&3\\-1&0&2\end{array}\right]\times\left[\begin{array}{ccc}2&-3\\1&0\\3&1\end{array}\right]}$

$\underline{\bold{Solution:}}$

$\bold{let\:A= \left[\begin{array}{ccc}-3&-1&3\\-1&0&2\end{array}\right] }\\\\\\\bold{B=\left[\begin{array}{ccc}2&-3\\1&0\\3&1\end{array}\right] }$

$\bold{AB=\left[\begin{array}{ccc}-3(2)+(-1)(1)+3(3)&-3(-3)+(-1)0+3(1)\\\\-1(2)+0(1)+2(3)&-1(-3)+0(0)+2(1)\end{array}\right] }\\\\\\\bold{AB=\left[\begin{array}{ccc}-6-1+9&9+0+3\\\\-2+0+6&3+0+2\end{array}\right] }$

$\bold{AB=\left[\begin{array}{cc}2&12\\\\4&5\end{array}\right] }$