Question

Evaluate NM if possible.

Answer 1

The MN matrix is $\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]$.

What is matrix?

A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that is used to represent a mathematical object or an attribute of one. is a matrix having two rows and three columns, for instance.

Given $M=\left[\begin{array}{cc} 1 & 0 \\ -4 & 3 \\ 2 & 5 \end{array}\right]$

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

M is a matrix with 3 * 2 dimension and N is a matrix with 2 * 3 dimension.

So finding MN is possible and the dimension will be 3 * 3.

Now,

$MN=\left[\begin{array}{cc}1 & 0 \\-4 & 3 \\2 & 5\end{array}\right] \times \left[\begin{array}{ccc}-2 & 1 & 0 \\3 & 2 & -1\end{array}\right]\\= \left[\begin{array}{ccc}1 \times (-2)+0 \times 3 & 1 \times 1+0 \times 2 & 1 \times 0+0 \times (-1) \\(-2) \times (-4)+3 \times 3 & (-4) \times 1+3 \times 2 & (-4) \times 0+3 \times (-1) \\2 \times (-2)+5 \times 3 & 2 \times 1+5 \times 2 & 2 \times 0+5 \times (-1) \\\end{array}\right]$

$=\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]$

Therefore the MN matrix is $\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]$.

To learn more about matrix from the given link

brainly.com/question/94574

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