Answer to Question #349092 in Linear Algebra for bel

Question

Let 𝐴=   1 1 1 3

               2 0 4 6

               1 1 3 7

a. What size is A?

b. What is the third column of A?

 c. What is the second row of A?

d. What is the element of A in the (3,2)th position?

e. What is A’?

Answer 1

𝐴=   1 1 1 3

        2 0 4 6

        1 1 3 7

a. There is a matrix with 3 rows and 4 columns, so the size is 3×4.

b. The third column of A is $\begin{bmatrix} 1 \\ 4 \\ 3 \end{bmatrix}$

c. The second row of A is $\begin{bmatrix} 2 & 0 & 4 & 6 \end{bmatrix}$

d. The element of A in the (3,2)th position (the third row, the second column) is 1.

e. To obtain A' we have to exchange rows and columns:

$A'=\begin{bmatrix} 1 & 2& 1 \\1 & 0 & 1\\1 & 4 & 3\\ 3 & 6 & 7 \end{bmatrix}$