Linear Algebra Answers

let

Matrix

A = 1 -1 1 B = 8 -3 -5

0 2 -1 0 1 2

2 1 3 4 -7 6

Compute A ^-1 , (B^T )^-1 and B^-1A^-1. What do you observe about

(7.1) (A ^-1 )^-1 in relation to A.

(7.2) ((B^T )^-1 ) T in relation to B^-1 .

(7.3) (AB) ^-1 in relation to B^-1 A^-1 .

Write notes on how to add, subtract and multiply matrices, and show how they may apply to solving a three system of equation , site examples on the applications of matrices to solving real world business problems

Examine linear inequalities and how to formulate their graphical solutions

1. Suppose v,w element of V. Explain why there exists a unique x element of V such that v +3x = w.

Show that if A is an n × n matrix, then AAT and A + A T are symmetric.

Show that if A is a matrix with a row of zeros (or a column of zeros), then A cannot have an inverse

Assume that A and B are matrices of the same size. Determine an expression for A if 2A − B = 5(A + 2B)

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.

(i) DC,

(ii) −CA + B,

(iii) CD − D

Suppose U={(x, x, y, y) ∈ F⁴ :x, y ∈ F}. Find a subspace W of F⁴=U ∅ W

Let S be a subset of F^{3 }defined as S={(x, y, z)∈F³ :x+y+z=4}.Then determine if S is a subspace of F³ or not