Question

Consider the following 2-by-4 matrix, which we call K. (The vertical bar is there simply as a visual aid to clearly separate the 2-by-2 matrices that we call A and I; otherwise, the bar has no significance)

K = [A|I] =
[ 2 31 0 1 4 70 il 2 31 14 7 ]

We simply took 2-by-2 matrices A and I, called them A and I respectively, and put them side-by-side to form the resulting 2-by-4 matrix K.

Consider also the matrices:
Ex = [ -2 1 ]
E12 = [ 63 ]

(a) Compute E21K.

Answer 1

The resulting matrix will be a 1-by-4 matrix i.e. E21K = [126, 1953, 0, 63].

Step-by-step explanation:

To compute E21K, we need to multiply the matrix E21 by the matrix K.

Since E21 is a 1-by-2 matrix and K is a 2-by-4 matrix, the resulting matrix will be a 1-by-4 matrix.

We can use matrix multiplication to find this product.

Each element of the resulting matrix will be the sum of the products of the corresponding elements in the rows of E21 and the columns of K.

Let's calculate the product:

E21K = [63] * [2 31 0 1; 4 70 -2 31]

E21K = [63 * 2 + 0 * 4, 63 * 31 + 0 * 70, 63 * 0 + 0 * -2, 63 * 1 + 0 * 31]

E21K = [126, 1953, 0, 63]