Linear Algebra Answers

solve the following system or show that it has no solutions
x+2y=7
-2x+y=1
x-y=-2
3x+y=6

find the inverse to the matrix

M = 2 -3
4 -5

and use this inverse to solve the system of equations
2x-3y=7
4x-5y=15

find the inverse to the matrix

1 -1 2
N= -1 3 2
2 1 -3

and use this inverse to solve the system of equations
x-y+2z=1
-x+3y+2z=1
2x+y-3z=5

The Routh Hurwitz criterion tells us that the eigenvalues of a 2x2 matrix A
with real entries have negative real parts if the determinant of A is positive and the
trace of A (the sum of the entries on the main diagonal) is negative. Prove this.

If x>1 & x>2 means x>2 in real line?

Either prove that this statement is always true, or give a counterexample to show that it may be false: If {v1,v2,...,vp} is a linearly dependent set of vectors in R^n, and x is any vector in R^n, then {v1,v2,...,vp,x} must also be linearly dependent.

3x-3y+z=1
-x+3y+2z=-4
x+3y+5z=-7
for the above system of linear equations find a solution and show that it has infinitely many
solution or show that it has no soultion

describe the column space (range ) and the nullspace (kernel) of the matrices
A= 1 -1 B= 0 0 0
0 0 0 0 0

Linear transformation
Is this linear trandformation?
L([x,y,z]) = [0,0,0]

Thank you!