find the product
[-5 -2 -8 -5] [-5 7 -9 -5]
To find the product of two matrices, we multiply corresponding elements from each matrix and then sum up the results. Here's how you can find the product of the given matrices:
Given matrices:
Matrix A = [-5 -2 -8 -5]
Matrix B = [-5 7 -9 -5]
Step 1: Calculate the element-wise multiplication
Multiply corresponding elements from each matrix:
[-5*(-5) -2*7 -8*(-9) -5*(-5)]
Simplifying the multiplications, we get:
[25 -14 72 25]
Step 2: Sum up the results
Add up the results from the previous step:
25 + (-14) + 72 + 25
Simplifying the addition, we get the final result:
108
Therefore, the product of the matrices is 108.
To find the product of the given matrices, we need to perform matrix multiplication.
The first matrix is represented by:
[-5 -2 -8 -5]
The second matrix is represented by:
[-5]
[7]
[-9]
[-5]
To find the product, we multiply the elements of each row in the first matrix with the corresponding element in each column of the second matrix and add them up.
For the first element in the resulting matrix, we have:
(-5)(-5) + (-2)(7) + (-8)(-9) + (-5)(-5) = 25 - 14 + 72 + 25 = 108
Continuing the process, we have:
[-5 -2 -8 -5] [-5 7 -9 -5] = [108 97 -95 40]
Therefore, the product of the given matrices is:
[108 97 -95 40]
To find the product of the given matrices, we will perform matrix multiplication.
First, let's label the matrices as A and B:
Matrix A:
[-5 -2 -8 -5]
Matrix B:
[-5 7 -9 -5]
To find the product AB, we will take the dot product of each row of A with each column of B and place the results into a new matrix.
To calculate the element at position (i, j) of the resulting matrix, we multiply the elements in the i-th row of matrix A with the corresponding elements in the j-th column of matrix B, and sum these products.
Let's calculate the product AB step by step:
Step 1: Calculate the element at position (1, 1) of the resulting matrix
(-5 * -5) + (-2 * -9) + (-8 * 7) + (-5 * -5) = 25 + 18 - 56 + 25 = 12
Step 2: Calculate the element at position (1, 2) of the resulting matrix
(-5 * 7) + (-2 * -5) + (-8 * -9) + (-5 * -5) = -35 + 10 + 72 + 25 = 72
Step 3: Calculate the element at position (1, 3) of the resulting matrix
(-5 * -9) + (-2 * -5) + (-8 * -5) + (-5 * -5) = 45 + 10 + 40 + 25 = 120
Step 4: Calculate the element at position (1, 4) of the resulting matrix
(-5 * -5) + (-2 * -5) + (-8 * -5) + (-5 * -5) = 25 + 10 + 40 + 25 = 100
Step 5: Repeat steps 1-4 for the remaining elements in the first row.
The resulting matrix AB is:
[12 72 120 100]
Therefore, the product of matrices A and B is:
[-5 -2 -8 -5] [-5 7 -9 -5] = [12 72 120 100]