find the product
[5 5 -2 3][-4 9 8 7]
The product of the given matrices is:
[5* -4 + 5* 9 + -2* 8 + 3* 7] = [-20 + 45 - 16 + 21] = 30
To find the product of these two matrices, we will perform matrix multiplication.
Given matrices:
A = [5 5 -2 3]
[-4 9 8 7]
B = [-4 9 8 7]
Matrix multiplication is performed by multiplying the corresponding elements of the rows of the first matrix with the corresponding elements of the columns of the second matrix and summing them up.
First, let's find the product of the first row of matrix A with the first column of matrix B:
A[1,1] * B[1,1] + A[1,2] * B[2,1] + A[1,3] * B[3,1] + A[1,4] * B[4,1]
= (5 * -4) + (5 * 9) + (-2 * 8) + (3 * 7)
= -20 + 45 - 16 + 21
= 30
Next, let's find the product of the first row of matrix A with the second column of matrix B:
A[1,1] * B[1,2] + A[1,2] * B[2,2] + A[1,3] * B[3,2] + A[1,4] * B[4,2]
= (5 * 9) + (5 * 9) + (-2 * 8) + (3 * 7)
= 45 + 45 - 16 + 21
= 95
Similarly, we can find the products of the second row of matrix A with both columns of matrix B:
Second row with first column:
A[2,1] * B[1,1] + A[2,2] * B[2,1] + A[2,3] * B[3,1] + A[2,4] * B[4,1]
= (-4 * -4) + (9 * 9) + (8 * 8) + (7 * 7)
= 16 + 81 + 64 + 49
= 210
Second row with second column:
A[2,1] * B[1,2] + A[2,2] * B[2,2] + A[2,3] * B[3,2] + A[2,4] * B[4,2]
= (-4 * 9) + (9 * 9) + (8 * 8) + (7 * 7)
= -36 + 81 + 64 + 49
= 158
Putting all the products together, we get the resulting matrix:
[30 95]
[210 158]
So, the product of the given matrices is:
[30 95]
[210 158]
To find the product of two matrices, you need to multiply the corresponding entries of each row of the first matrix with the corresponding entries of each column of the second matrix and then sum up the results.
Given the matrices:
A = [5 5 -2 3]
B = [-4 9 8 7]
To find the product of A and B, you need to multiply the individual entries as follows:
- For the first entry of the product matrix, multiply the first entry of the first row of A (which is 5) with the first entry of the first column of B (which is -4): 5 * -4 = -20.
- For the second entry of the product matrix, multiply the first entry of the first row of A (which is 5) with the second entry of the second column of B (which is 9): 5 * 9 = 45.
- For the third entry of the product matrix, multiply the first entry of the first row of A (which is 5) with the third entry of the third column of B (which is 8): 5 * 8 = 40.
- For the fourth entry of the product matrix, multiply the first entry of the first row of A (which is 5) with the fourth entry of the fourth column of B (which is 7): 5 * 7 = 35.
Repeat the same process for the second entry of A's first row and second row, and so on.
After performing these calculations, the resulting product matrix will have a single row and four columns, with the respective entries:
[-20 45 40 35]
Therefore, the product of the given matrices is:
[-20 45 40 35]