Suppose that A, B, C, D, and E are matrices with the following sizes: A B C D E
(4x 1) (4 x 1) (1 x 2) (2 x 1) (1 x 4)
Determine whether the matrix expression E (3B + A) is defined. Matrix is defined Enter the size of the resulting matrix (enter 'NA in each box if undefined).
E (3B + A) is a 3 X 3.

The expression E (3B + A) is defined. The size of the resulting matrix is (1 x 1).

Step-by-step explanation:

Let's consider the following operations between matrices.

E (3B + A)

B is a matrix of (4 x 1), that is, it has 4 rows and 1 column. Let F = 3B. This is the product of a scalar by a matrix, which results in a matrix of the same size as the original. Then, F is a matrix of (4 x 1).

Now, let's consider the sum F + A, which we well call G. We can sum F and A because they are of the same size and we will get G, a matrix of the same size, (4 x 1).

Finally, we have the product E . G. We can multiply 2 matrices of sizes (m x k) and (k x n), that is, the number of columns of the first matrix must be equal to the number of rows of the second matrix, and the resulting matrix has a size (m x n). This is the case because E is (1 x 4) and G is (4 x 1), and the resulting matrix will be (1 x 1).

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