find the product
[-5 -2] [-5 7]
[-8 -5] [-9 -5]
The product of the two matrices is:
[-5 * -5 + -2 * -9, -5 * 7 + -2 * -5]
[-8 * -5 + -5 * -9, -8 * 7 + -5 * -5]
Simplifying,
[25 + 18, -35 + 10]
[40 + 45, -56 + 25]
[43, -25]
[85, -31]
To find the product of two matrices, follow these steps:
Step 1: Make sure the number of columns in the first matrix is equal to the number of rows in the second matrix. If they are not equal, you cannot perform matrix multiplication.
Step 2: Multiply the corresponding elements from each row of the first matrix with the corresponding elements from each column of the second matrix. Add the results to find the elements of the resulting matrix.
Let's apply these steps to the given matrices:
First, we have the matrices:
A = [-5 -2] B = [-5 7]
[-8 -5] [-9 -5]
To find the product AB, we need to make sure that the number of columns in matrix A is equal to the number of rows in matrix B. In this case, both matrices have 2 columns and 2 rows, so we can proceed with the multiplication.
Next, let's find the elements of the resulting matrix by multiplying and adding the corresponding elements as described in step 2:
First element of the resulting matrix:
(-5*-5) + (-2*-9) = 25 + 18 = 43
Second element of the resulting matrix:
(-5*7) + (-2*-5) = -35 + 10 = -25
Third element of the resulting matrix:
(-8*-5) + (-5*-9) = 40 + 45 = 85
Fourth element of the resulting matrix:
(-8*7) + (-5*-5) = -56 + 25 = -31
So, the product of matrices A and B is:
AB = [43 -25]
[85 -31]
To find the product of two matrices, you need to multiply each element of the first matrix by the corresponding element in the second matrix, and then sum them up.
Given the matrices:
Matrix A:
-5 -2
-8 -5
Matrix B:
-5 7
-9 -5
To find the product of these matrices, follow these steps:
Step 1: Multiply the corresponding elements of the matrices:
-5 * -5 = 25
-2 * 7 = -14
-8 * -9 = 72
-5 * -5 = 25
Step 2: Sum up the products:
25 + (-14) = 11
72 + 25 = 97
The product of Matrix A and Matrix B is:
11 97