Linear Algebra Answers

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

Suppose v_1,v_2,........,v_{m }is a linearly independent in V and w∈V. Show that v_1,v_2,........,v_{m }is linearly independent if and only if w∉span(v_1,v_2,........,v_{m )}

one to one correspondence functions