Linear Algebra Answers

Find the inverse of matrix A given below using the formula A ^-1 =C^T/│A│

A="\\begin{vmatrix}\n -6 & -4 & -4 \\\\\n -1 & -4 & 6 \\\\\\\n-6 & 5 & -1\n\\end{vmatrix}"

Solve for the determinant in the equation below.

4 −3 2

1 2 −2

2 -1 −4

Solve the following equation using inverse method

[1 3 0] [x] [4]

[0 0.5 1] [y]=[1]

[0.5 0 1] [z] [3]

2x+y-z=8

-3x-y+2z=-11

-2x+y+2z=-3

D. Cramer’s Rule; 1. 6x+3y= 6; 5x-3y=3 2. 2x-3y=5; 4x+10y=4

Which of the following sets of polynomials span P2 ?

a. {t²+1, t-1, t²+t}

B. {t²+ 2, 2t²- t+1, t + 2 , t²+t+4}

Let V = set of all 3x1 matrices.

Define

+ to be the matrix addition

⦁ to be the matrix multiplication by a number

We know that V is a vector space. If W [a, b, 1] , a, b element of R then W is a subspace of V.

Let V be the set of all positive real numbers; define + by u+v = uv (+ is ordinary multiplication) and define • by c•v = . Prove that V is a vector space.

1. For what values of h the vectors

⟶ [ 1 ⟶ [ -1 ⟶ [ 5

u = -3 u_{2 =} 9 u₃ = -7 <--- u₁, u₂, and u₃ are vectors

-2] -6] h]

are linearly independent?