Linear Algebra Answers

Use GAUSS-JORDAN INVERSE METHOD to solve these systems of Linear Equations.

y-10z=-8

2х - бу=8

x+2z=7

Show that for any g element of L(V;C) and u element of V with g(u) not equal 0: V =null g operation { xu: x element of C}

Let V be the vector space of all 2×2 matrices over the field R. let W₁ = {"\\begin{bmatrix}\n x & -x \\\\\n y & z\n\\end{bmatrix}"| x,y,z€R} and W₂= {"\\begin{bmatrix}\n a & b \\\\\n -a & c\n\\end{bmatrix}"| a,b,c€R}. What is the dimensions of W₁+W₂ and W₁ intersection W₂ as well?

Find det(-2A) and compare it to det(A) for A=[-2 1 3][1 4 5][2 3 1]

Find the det(-2A) and compare it to det(A) for A={1 1}{3 -1}

Use GAUSS-JORDAN INVERSE METHOD to solve these system of Linear Equations.

y-10z=-8

2x-6y=8

x+2z=7

Prove that the dot between two vectors is commutative not associative

Find the determinant and inverse of:

  a)

3 0

5 9

  b)  

−3 7 9

1 1 3

4 9 3

Check whether T(x1,x2,x3)=(x1+x2/x3,x3) define linear transformation from R3 to R2

determine whether or not the set of vectors {(1,2,-1),(0,3,1),(1,-5,3)} is a basis of R^3 also find dimension