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 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.
The first matrix has dimensions 1 x 4, meaning it has 1 row and 4 columns.
The second matrix has dimensions 2 x 1, meaning it has 2 rows and 1 column.
Since the number of columns in the first matrix (4) is equal to the number of rows in the second matrix (2), 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. Therefore, the product matrix will have dimensions 1 x 1.
The product of two matrices is defined if the number of columns in the first matrix is equal to the number of rows in the second matrix.
Let's consider the given matrices:
Matrix A has dimensions 1x4 (1 row, 4 columns): [4 5 9 -2]
Matrix B has dimensions 2x1 (2 rows, 1 column): [1 7]
Since the number of columns in matrix A (4) is not equal to the number of rows in matrix B (2), the product AB is not defined.
To determine whether the product of two matrices 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. If they are equal, then the product is defined; otherwise, it is undefined.
In this case, we have the first matrix:
[4 5 9 -2]
and the second matrix:
[1]
[7]
The first matrix has 4 columns, and the second matrix has 2 rows. Since the number of columns in the first matrix (4) is not equal to the number of rows in the second matrix (2), the product is undefined.
Therefore, the product matrix does not exist, and we cannot determine its dimensions.