Exercise 3.16: Matrix

Exercise 3.16

1. In the matrix A = , write

(i) The number of elements

(ii) The order of the matrix

(iii) Write the elements a22, a23, a24, a34, a43, a44 .

2. If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?

3. Construct a 3 ×3 matrix whose elements are given by

(i) aij = |i − 2j| (ii) aij = (i+j)3/3

4. If   then find the transpose of A.

5. If  then find the transpose of -A .

6. If A =  then verify (AT)T = A

7. Find the values of x, y and z from the following equations

Answers:

1.(i) 16 (ii) 4 × 4 (iii) √7 , √3/2 , 5, 0, -11 , 1

2.1 × 18 , 2 × 9 , 3 × 6 , 6 × 3 , 9 × 2 , 18 × 1 and 1 × 6, 2 × 3, 3 × 2, 6 × 1

7.(i) 3,12,3 (ii) 4,2,0 or 2,4,0 (iii) 2,4,3