[9 4]is the top part of the first matrix, [2 1] is the bottom part of the first matrix. X= is between both matrixes. [-9 -6] is the top part of the second matrix [-1 -8] is the bottom part of the second matrix.
(answer is a matrix)
To compute the matrix multiplication, we multiply each element in the row of the first matrix by the corresponding element in the column of the second matrix and sum them up.
Therefore, the matrix multiplication [9 4; 2 1] x [-9 -6; -1 -8] is:
[(9)(-9) + (4)(-1) (9)(-6) + (4)(-8)]
[(2)(-9) + (1)(-1) (2)(-6) + (1)(-8)]
Simplifying this gives:
[-81 + (-4) -54 + (-32)]
[-18 + (-1) -12 + (-8)]
[-85 -86]
[-19 -20]
So, the resulting matrix is [-85 -86; -19 -20].
To find the product of two matrices, we need to multiply corresponding elements of the rows in the first matrix with the columns in the second matrix. Given the matrices:
Matrix A = [[9, 4], [2, 1]]
Matrix B = [[-9, -6], [-1, -8]]
Let's perform the matrix multiplication step by step:
Step 1: Multiply the first element of the top row of Matrix A with the first element of the top column of Matrix B:
First element: (9 * -9) + (4 * -1) = -81 - 4 = -85
Step 2: Multiply the second element of the top row of Matrix A with the second element of the top column of Matrix B:
Second element: (9 * -6) + (4 * -8) = -54 - 32 = -86
Step 3: Multiply the first element of the bottom row of Matrix A with the first element of the top column of Matrix B:
Third element: (2 * -9) + (1 * -1) = -18 - 1 = -19
Step 4: Multiply the second element of the bottom row of Matrix A with the second element of the top column of Matrix B:
Fourth element: (2 * -6) + (1 * -8) = -12 - 8 = -20
Combine the results to form the resulting matrix:
Resulting matrix: [[-85, -86], [-19, -20]]
Therefore, the product of the two matrices is:
[[-85, -86],
[-19, -20]]
To find the product of the two matrices, we will use the matrix multiplication rule.
First, let's label the matrices:
Matrix A:
| 9 4 |
| 2 1 |
Matrix B:
| -9 -6 |
| -1 -8 |
To calculate each element of the resulting matrix, we will multiply the corresponding elements of each row in Matrix A with each column in Matrix B and sum them up.
The resulting matrix will have dimensions 2x2, as Matrix A is 2x2 and Matrix B is also 2x2.
Using the matrix multiplication rule, the resulting matrix will be:
| (9 * -9 + 4 * -1) (9 * -6 + 4 * -8) |
| (2 * -9 + 1 * -1) (2 * -6 + 1 * -8) |
Simplifying the calculations, we get:
| (-81 - 4) (-54 - 32) |
| (-18 - 1) (-12 - 8) |
Which further simplifies to:
| -85 -86 |
| -19 -20 |
Therefore, the resulting matrix is:
| -85 -86 |
| -19 -20 |