Linear Algebra Answers

Let W1 and W2 be subspaces of a vector space V and define
W1 + W2 := {u+v : u ∈ W1, v ∈ W2}.
Prove that span(W1 U W2) = W1 + W2.

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Solve for a

If A.x=
λx
,where A=
∣∣∣∣211232−212∣∣∣∣
,determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If
λ=1
,what is a

Solve the linear equations 2x+4y=10 and 3x+6y=15

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c

Please prove the following lemma by showing that if M > N, then there is a non-zero vector x such that Cx = Ax = 0:

lemma: Let W = {w^1,...,w^N} be a spanning set for a subspace S in R^I, and let {v^1,...,v^M} be a linearly independent subset of S. then M <= N.

We have W = {w^1,...,w^n} as a spanning set for a subspace S in R^j, and V = {v^1,...,v^m} a linearly independent subset of S. Let A be the matrix whose columns are the v^m, B the matrix whose columns are the w^n. Please show that there is an N by M matrix C such that A = BC.

Show that if L is invertible and lower triangular, then so is L^(-1).

can u please help me solve this equation. i have the answer in my book but can u help me solve it
i have a 3x3 matrix
1=p(1,1) + p(2,1)*e^ix + p(3,1)*e^-ix
cos x = p(2,1) + p(2,2)*e^ix +p(3,2)*e^-ix
sin x= p(1,3) +p(2,3)*e^ix + p(3,3)*e^-ix
where p is a 3 by 3 matrix

maximize z=5x+2y
Subject to 5x-y <15
2x + y >10
x > 3
y < 8
name the maximum value and the points