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 ).
Suppose 𝑋 is a matrix such that
𝑋 + 𝑋 2 = −𝐼𝑛
Find 𝑑𝑒𝑡 𝑋
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)