Linear Algebra Answers

Prove that there does not exist a linear map T : R5 - R5 such that range T = null T.

Suppose b,c element of R, and T: R³ - R² dened as T (x;y;z) = (2x4y+3z+b,6x+cxy): Show that T is linear if and only if b = c = 0.

Suppose V is finite-dimensional with dim V ≥ 2.

Prove that there exist S, T ∈ L(V; V ) such that ST ≠ T S.

please assist.

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