Linear Algebra Answers

determine if the set is a subspace of r2 or not

{ x: (x1,x2) such that x1= -x2 }

is this a subspace ?
.

Solve the following matrix by Gaussian Model

1.) -4x + y = 3
3x - 5y = 0


2.) 3x + 4y + 5z = -9
2x - 3y + 3z = -1
x + 2y - 4z = -15

Solve the matrix of the following using the Gaussian Method.

1. 3x-5y= -2
2x+4y= 7

Show that the vectors (1-i,i) and (2,-I+i) in R² are Linearly Dependent over Field R but Linearly Independent over R , where i = √-1

Show that the vectors (1-I,i) and (2,-I+i) in R² are Linearly Dependent over Field but Linearly Independent over R , where .i = √-1

Let A be an n×n matrix. Then Show that the set, U={uϵRn : Au = - 3un} is a Subspace ofRn

Find the inverse of the matrix
1 −1 0
2 −1 1
1 1 −1

using row reduction.

Let B1 ={(1,1),(1,2)} and B2 ={(1,0),(2,1)}. Find the matrix of the change of basis from B1 to B2

Which of the following matrices are Hermitian and which are Unitary? Justify your answer.


A = 1 i 0 B= 1/√2 0 -1/√2
-i 1 1-i 0 1 0
0 1+i 2 V2i 0 V2i