[[1,1,-4],[5,6,0]]*[[9],[1],[-7]]
determine whether the product is defined or undefined. if defined give the dimensions of the product matrix
To multiply two matrices, the number of columns of the first matrix must be equal to the number of rows of the second matrix.
In this case, the first matrix has dimensions 2x3, and the second matrix has dimensions 3x1.
Therefore, the product is defined, and the dimensions of the product matrix will be 2x1.
To determine if the product of the 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 2x3 (2 rows and 3 columns).
The second matrix has dimensions 3x1 (3 rows and 1 column).
Since the number of columns in the first matrix is equal to the number of rows in the second matrix (3 = 3), the product is defined.
The product matrix will have dimensions 2x1 (2 rows and 1 column).
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.
In this case, the first matrix has 2 columns, and the second matrix has 3 rows. Since the number of columns in the first matrix does not match the number of rows in the second matrix, the product of these matrices is undefined.
Therefore, the product is undefined and there are no dimensions for the product matrix.