Linear Algebra Answers

Express (7,0,9) as a linear combiantion of v1(1,1,1) v2(1,1,0) and v3(1,0,0)

Solve the inequality √(x²-2x-8) ≤ -x+2

if w is subspace of a vector space V over field F such that dim v=5 and dim w=2 then dim A(w) =

Given a number 𝑑 = 𝑑𝑒𝑡(𝐴1, ⋯ , 𝐴𝑛 ), find 𝑑𝑒𝑡(𝐴𝑛, ⋯ , 𝐴1 ).

Given a number 𝑑 = 𝑑𝑒𝑡(𝐴1, ⋯ , 𝐴𝑛 ), find 𝑑𝑒𝑡(𝐴𝑛, ⋯ , 𝐴1 ).

Express V= 3t² + 7t + -4 as a linear combination of the polynomials

P1= t² + 2t + 3

P2= 2t² + 3t + 7

P3 = 3t² + 5t + 6

Determine whether the vectors are linearly dependent or independent (1,2,1),(-1,0,1) and (2,-1,4)

Let f:R²→R² be defined by f(x,y)=(-y,-x)

i) show that f is linear

ii)Determine a basis for the kernel of f and the nullity of f

iii) Determine the basis for the range of f and the rank of f

iv) Determine whether f is invertible or not

Construct an orthonormal basis for the subspace of R³ spanned by the vectors (1,-1,1)

and (2,0,4)