B-A
A=[[-5,4],[-8,2]] B=[[-2,7,-3],[1,-6,0]]
The product of matrices B and A is:
B x A = [[-2, 7, -3], [1, -6, 0]] x [[-5, 4], [-8, 2]]
To calculate this product, we multiply the rows of B with the columns of A:
[-2, 7, -3] x [-5, -8] = (-2*-5) + (7*-8) + (-3*4) = 10 - 56 - 12 = -58
[-2, 7, -3] x [4, 2] = (-2*4) + (7*2) + (-3*4) = -8 + 14 - 12 = -6
[1, -6, 0] x [-5, -8] = (1*-5) + (-6*-8) + (0*4) = -5 + 48 + 0 = 43
[1, -6, 0] x [4, 2] = (1*4) + (-6*2) + (0*4) = 4 - 12 + 0 = -8
Therefore, the product of matrices B and A is:
B x A = [[-58, -6], [43, -8]]
To calculate the product B-A, follow these steps:
Step 1: Check if the matrices can be multiplied.
- For two matrices to be multiplied, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, matrix A has 2 columns and matrix B has 2 rows, so they can be multiplied.
Step 2: Multiply the matrices element by element.
- To find the element in the resulting matrix B-A, subtract the corresponding elements from matrix A from the corresponding elements in matrix B.
B-A = B - A =
[[-2, 7, -3], [1, -6, 0]] - [[-5, 4], [-8, 2]]
Step 3: Perform subtraction.
- Subtract the corresponding elements from matrix A from the corresponding elements in matrix B.
B - A = [[-2 - (-5), 7 - 4, -3 - 0], [1 - (-8), -6 - 2, 0 - 0]] =
[[3, 3, -3], [9, -8, 0]]
Therefore, the resulting matrix B-A is:
B-A = [[3, 3, -3], [9, -8, 0]]
It seems like you have provided two matrices: Matrix A and Matrix B. Matrix A is a 2x2 matrix, while Matrix B is a 2x3 matrix.
To get the result of the matrix multiplication between Matrix A and Matrix B, you need to perform the dot product of the corresponding rows and columns. Here's how you can do it:
1. Multiply the first row of Matrix A by the first column of Matrix B:
A[0][0] * B[0][0] + A[0][1] * B[1][0] = -5 * -2 + 4 * 1 = 10 + 4 = 14
2. Multiply the first row of Matrix A by the second column of Matrix B:
A[0][0] * B[0][1] + A[0][1] * B[1][1] = -5 * 7 + 4 * -6 = -35 - 24 = -59
3. Multiply the first row of Matrix A by the third column of Matrix B:
A[0][0] * B[0][2] + A[0][1] * B[1][2] = -5 * -3 + 4 * 0 = 15 + 0 = 15
4. Multiply the second row of Matrix A by the first column of Matrix B:
A[1][0] * B[0][0] + A[1][1] * B[1][0] = -8 * -2 + 2 * 1 = 16 + 2 = 18
5. Multiply the second row of Matrix A by the second column of Matrix B:
A[1][0] * B[0][1] + A[1][1] * B[1][1] = -8 * 7 + 2 * -6 = -56 - 12 = -68
6. Multiply the second row of Matrix A by the third column of Matrix B:
A[1][0] * B[0][2] + A[1][1] * B[1][2] = -8 * -3 + 2 * 0 = 24 + 0 = 24
Putting it all together, the result of the matrix multiplication between Matrix A and Matrix B is:
[[14, -59, 15],
[18, -68, 24]]
So, B-A is equal to:
[[-5,4],[-8,2]] - [[-2,7,-3],[1,-6,0]] = [[14, -59, 15], [18, -68, 24]]