Answer:
-3 11 This is the 4th and last answer choice.
-19 13
Explanation:
Matrix multiplication has its own rules!
Here you have two 2x2 matrices: 2 rows, 2 columns each. Because the number of rows of the first matrix (2) matches the number of columns of the second matrix (also 2), we know we can find the matrix product, and that its dimensions will be 2 rows by 2 columns (same as the dimensions of X and Y).
Ready? We'll find the sum/product that goes into the first row, first column of the matrix we'll call XY. Take that 3 in the first row of X and multiply it by -2, which you find in the first row, first column of Y. Continuing, multiply -3 in the 2nd row, 1st column of Y by -1, which is in the first row, 2nd col. of X. Now add together these products: add together (3)(-2) and (-1)(-3), obtaining -6+3, or -3. This goes into the first row, first column of your product vector XY.
Now multiply the 2nd column of Y with the first row of X. We get:
(3)(4) + (-1)(1), or 11. This goes into the 1st row, 2nd column of XY:
XY is now -3 11 and we must still determine the 2nd row of XY.
Multiply the first col. of Y by the 2nd row of X, obtaining (2)(-2) + (5)(-3), or
-4 - 15, or -19.
Finally, mult. the 2nd col. of Y by the 2nd row of X, obtaining:
(2)(4) + (5)(1), or 8 + 5 = 13. Now we've finished all the multiplications, and have the new product matrix XY which is equal to the following:
-3 11
-19 13
Again, this is matrix multiplication.