Linear Algebra Answers

Determine whether the set S is subspace of R5 defined by

S = f(x1; x2; x3; x4; x5) R5

: x1 = 3x2 and x3 = 7x4:

find the value of x if A = [[x, 2], [4, 3]] and A ^ - 1 = [[- 1/2, 1/3], [2/3, 0]]

Given that the set S= ((1,0,0,0), (0,0,1.0), (5,1,11,0), (-4,0,-6,1)) is a basis of R*, and T= {(1,0,1,0), (0,2,0,3)} is linearly independent. Extend T to a basis of R.

Let T be the linear operator on R

2 defined by

T(x, y) = (−y, x)

i. What is the matrix of T in the standard ordered basis for R2 ?

ii. What is the matrix of T in the ordered basis B = {α1, α2}, where α1 = (1, 2) and α2 = (1, −1)?

iii. Prove that for every real number c the operator (T − cI) is invertible.

Show that 𝑊 = {(𝑥, 4𝑥, 3𝑥) ∈ ℝ2 |𝑥 ∈ ℝ} is a subspace of ℝ 3 . Also find a basis for subspace 𝑈 of ℝ 3 which satisfies 𝑊 ⊕ 𝑈 = ℝ3

let a be a 2 cross 3 matrix b be a 3 cross 4 Matrix and C be 3 cross 2 Matrix and d be a 3 cross 4 matrix. is ab + ctd defined? justify your answer.

 State the domain and range of the following function 𝑓(𝑥) = 1/(𝑥−1) + 2

c) Martin, Arop and Sam and went shopping at Kabale mega super market buying similar items. Martin bought one kilogram of sugar and one tin of blue band spending 6 shillings altogether. Arop bought bought 3 kilograms of maize flour and one tin of blue band spending 17 shillings altogether. Sam bought two kilograms of sugar, one kilogram of maize flour and 3 tins of blue band spending 15 shillings altogether. i) Express their purchases as equations ii) Using matrix method, find the cost of each kilogram of sugar, maize flour and a tin of blue band.

let B={1-t,t-t²,2-2t+t²} be an ordered basis for p₂

let p(t)=3+t-6t²

1. find [p(t)]_B

1.Which of the following is the solution of the equation below?

0x + 0y = 0

1. (0,0,0).

2. (1,0,0).

3. No such solution exists

4. Infinitely many solution or (-1,2,1).