Question

What is the product??? A scalar and matrix problem.

Answer 1

OPTION 3!

Explanation:

We need to multiply 1st row by the 1st column:

(1*2)+(3*3)+(1*4)=2+9+4=15

Now the 2nd row by the 1st column:

(1*-2)+(3*5)+(1*1)=-2+15+14

So the first row of the new matrix is 15 and 14, and that's option 3!

Answer 2

`\left[\begin{array}{ccc}15&14\\-1&9\end{array}\right]`

Explanation:

To perform this product, you need to orderly multiply the elements of a row of the first matrix times the elements of a column in the second matrix, and add the individual products.

The rows and columns that need to be multiplied to populate the for elements of the resulting matrix are highlighted in different colors in the attached image.

Here I give you the product and addition results for each element:

For the element in red: 1*2 + 3*3 +1*4 =2+9+4=15

For the element in green: 1*(-2)+3*5+1*1=-2+15+1 = 14

For the element in blue: (-2)*2+1*3+0*4=-4+3+0 = -1

For the element in brown: (-2)*(-2)+1*5+0*1= 4+5+0= 9