Question

PLS HELP ME. URGENT ASSISTANCE NEEDED. I have no clue what I'm doing.

Multiply the given matrices.

Answer 1

`\left[\begin{array}{cc}21&60\\10&-31\end{array}\right]`

Explanation:

When multiplying two matrices, we need to take the dot product of the corresponding row from the first matrix and column from the second matrix.

The dot product is where we multiply corresponding elements of a row from the first matrix and a column from the second matrix, then add them together to produce a single element in the resulting matrix.

Given expression:

`\left[\begin{array}{rrr}3&-6&7\\-4&2&-1\end{array}\right]\cdot \left[\begin{array}{rr}-3&5\\2&-4\\6&3\end{array}\right]`

Multiply the rows of the first matrix by the columns of the second matrix.

For example, multiply the first element of the first row (3) by the first element of the first column (-3), then add this to the product of the second element of the first row (-6) and the second element of the first column (2), then add this to the product of the third element of the first row (7) and the third element of the first column. The result is placed in the top left position in the resulting matrix. We then continue in this way by multiplying elements of the first row of the first matrix by elements of the second column of the second matrix, and placing the result in the top right position in the resulting matrix.

Therefore, taking the dot product of the rows and columns gives:

`=\left[\begin{array}{cc}(3\cdot-3)+(-6\cdot 2)+(7\cdot 6)&(3\cdot5)+(-6\cdot-4)+(7\cdot3)\\(-4\cdot-3)+(2\cdot2)+(-1\cdot6)&(-4\cdot5)+(2\cdot -4)+(-1\cdot3)\end{array}\right]`

Simplify:

`=\left[\begin{array}{cc}-9+(-12)+42&15+24+21\\12+4+(-6)&-20+(-8)+(-3)\end{array}\right]`

`=\left[\begin{array}{cc}-9-12+42&15+24+21\\12+4-6&-20-8-3\end{array}\right]`

`=\left[\begin{array}{cc}21&60\\10&-31\end{array}\right]`