Linear Algebra Answers

Consider the matrices A =   3 0 2 4 −6 3 −2 1 8   ,B =   −5 1 1 0 3 0 7 6 2   , C =   1 1 1 2 3 −1 3 −5 −7   , Verify the following expressions (where possible and give reasons) (i) A + (B + C) = (A + B) + C and A(BC) = (AB)C. (ii) (a − b)C = aC − bC and a(B − C) = aB − aC, where a = −2, b = 3 . (iii) (A T ) T = A and (A − B) T = A T − B T .

Let P(x) = x 2 − x − 6. Compute P(A) for A =  3 −1 0 −2 

Solve for x, y, z, and t in the matrix equation below.  3x y − x t + 1 2 z t − z  =  3 1 7 2 3  .

Suppose that A, B, C, and D are matrices with the following sizes: A (5 × 2), B (4 × 2), C (4 × 5), D (4 × 5) Determine in each in each of the following case whether a product is defined. If it is so, then give the size of the resulting matrix. [6] (i) DC, (ii) −CA + B, (iii) CD − D.

A basketball team has to raise $750 for new uniforms. The players have raised $150 from food sales. To raise the rest, they are holding a shoot-out challenge. In total, 30 teams have signed up. How much should each team pay

Using GAUSS –JORDON Method, find the Inverse of the following matrix :

1 2 -1 4

2 3 2 0

3 1 0 3

2 0 2 1

The cat food is sold in tins containing 500 g.

Write down the matrix M such that the product XM will show, for each brand,

the total cost, in cents, of buying ten tins at both stores during May.

Find all values of lemth€C such that lemth(1+2i, 5+4i) =(3+2i, 6-i)

Show that in the definition of a vector space v the condition about existence of additive inverse can be replaced with the condition:0v=v for all v€V

What are the domain and range for these equations?

1. f(x)= square root of (x-1)
2. f(x)=6x-1/1-2x
3. the inverse of function f(x) = square root of (x-1)