Find the product.
[5 5];[-2 3]*[-4 9];[8 7]
The product of [5 5];[-2 3] and [-4 9];[8 7] is not defined because matrix multiplication is only defined for matrices with compatible dimensions. In this case, the first matrix has dimensions 2x2 and the second matrix has dimensions 2x2, so matrix multiplication is not possible.
To find the product of two matrices, you need to multiply the corresponding elements and sum up the results. Here's how to calculate the product of the given matrices.
First, let's multiply the first and second matrices:
[5 5] * [-2 3] = [(5 * -2) + (5 * 3)] = [-10 + 15] = 5
Next, let's multiply the result from the previous step by the third matrix:
5 * [-4 9] = [5 * -4, 5 * 9] = [-20, 45]
Finally, let's multiply the result from the previous step by the fourth (last) matrix:
[-20, 45] * [8 7] = [(8 * -20) + (7 * 45)] = [-160 + 315] = 155
Therefore, the product of the given matrices is 155.
To find the product of the given matrices, we perform matrix multiplication.
First matrix: [5 5]
Second matrix: [-2 3]
Third matrix: [-4 9]
Fourth matrix: [8 7]
To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, the first matrix has 2 columns and the second matrix has 2 rows, so multiplication is possible.
The product of the first two matrices can be found as:
[5 * -2 + 5 * -4 5 * 3 + 5 * 9]
[ ]
[= -10 + -20 15 + 45 ]
[ ]
[= -30 60 ]
Now, we need to multiply this result by the third matrix:
Product = [-30 60] * [8 7]
To do this multiplication, we again ensure that the number of columns in the first matrix matches the number of rows in the second matrix. In this case, the first matrix has 2 columns and the second matrix has 1 row, so multiplication is possible.
The product of these matrices can be found as:
[-30 * 8 + 60 * 7]
[= -240 + 420 ]
[= 180 ]
Therefore, the product of [5 5];[-2 3]*[-4 9];[8 7] is 180.