Linear Algebra Answers

find a linear transformation T:R^3->R^3 whose image is spanned by (1,2,3 ) and (4,5,6)

. let t:r^2->r^2 be a linear transformation for which ( 1,2)= (2,3 ) and ( 0,1)= (1,4 ). find a formula for t.

find basis and dimension of the subspace W of V spanned by A = [[1 2] [-1 3]], B = [[2 5] [1 -1]], C = [[5 12] [1 1]], D= [[3 4] [-2 5]]

Let T be an element of L(R³) such that-4,5,"7" are it eigenvalues. show that T(x)-9x=(-4,5,"7" )

Let W = {(X1, X2, X3) €R³: X2 + X3 = 0}. How do I show that W is a subspace of R³? What are two subspaces W1 and W2 of R³ such that R³=W⊕W1and R³=W⊕W2 but W1≠W2?