ORM2001 1. DEMOS (week 3)

1. Here you can see two matrices, A (left) and B (right).

Solve:

a) AT (the transpose of A)

b) AAT

c) A + B and A - B

d) AB and BA

e) AA and AAA

2. Below is a matrix A, and two vectors, x and y. Solve:

a) Ax

b) xTA

c) xyT

d) x Ty

3. Solve the following equations by Gauss-Jordan method:

a)

+ x1 - x 2 + x3 + x 4 = 3

+ 2x2 - x3 - 2x4 = 2

+ x2 + x3 - x 4 = 4

+ x1 + x 2 + x 3 - 4x 4 = 0

b)

+ x1 + 2x 2 - x 3 = 3

- 2x1 - x 2 = -4

- x1 + x 2 - x 3 = 1

4. Solve S C1k CT k2, when k grows from 1 to 2.

5. What is the inverse of a matrix A? What about the inverses of B and C?:

Matrix: Solve these before you hear a telephone ringing....