Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix.
[4 5];[9 -2] [1 7]
To determine whether the product is defined, we need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
The first matrix [4 5] has 2 columns.
The second matrix [9 -2] [1 7] has 2 rows.
Since the number of columns in the first matrix is equal to the number of rows in the second matrix, the product is defined.
To find the dimensions of the product matrix, we take the number of rows from the first matrix and the number of columns from the second matrix.
The product matrix will have 2 rows and 2 columns.
To determine whether the product is defined or undefined, we need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
Given the first matrix [4 5; 9 -2] which has 2 rows and 2 columns, and the second matrix [1 7], which has 1 row and 2 columns.
Since the number of columns in the first matrix is equal to the number of rows in the second matrix (2 = 2), the product of these matrices is defined.
To find the dimensions of the product matrix, we take the number of rows of the first matrix and the number of columns of the second matrix. In this case, the product matrix will have 2 rows and 2 columns.
To determine if the product of two matrices is defined, we need to check if the number of columns in the first matrix is equal to the number of rows in the second matrix.
Let's label the matrices:
Matrix A = [4 5]
[9 -2]
Matrix B = [1 7]
Matrix A has dimensions 2x2 (2 rows and 2 columns), and Matrix B has dimensions 2x1 (2 rows and 1 column).
To calculate the product of A and B, we multiply each element of the first row of A by the corresponding element in the first column of B and add them together. Since both A and B have the same number of rows, the product will have the same number of rows.
Calculating the product:
Row 1 of A: [4 5]
Row 1 of B: [1]
Product: (4x1) + (5x7) = 4 + 35 = 39
So, the product of A and B is a 2x1 matrix.
Therefore, the product is defined, and the dimensions of the product matrix are 2x1.