Linear Algebra Answers

Suppose T "\\isin" L(R²) is dened by T(x,y) = (-3y,x). Find the eigenvalues of T.

Show that if S and T are linear

transformations on a finite dimensional

vector space, then rank (ST)<= rank (S).

Show that if S and T are linear

transformations on a finite dimensional

vector space, then rank (ST)<= rank (S).

Determine whether the given line and the given plane are parallel :

a.) x = 1 + t, y=-1, z=-2t and x = 2y +3z - 9 =0,

b.) <0, 1, 2> +t <3,2,-1> and 4x - 2z +1 = 0

Let T element of L(R³ ) such that -4, 5 and square root 7 are its eigenvalues.

Show that T(x) - 9x = (-4, 5, square root 7).

Prove that every finite dimensional space has a basis

Let S = {α, β, γ}, T = {α, α + β, α + β + γ}, W = {α + β, β + γ, α + γ} be subsets in (4)

a vector space V. Prove that L(S ) = L(T) = L(W).

Question 1

Stonewall receives ¢250 per year in simple interest from an amount of money he invested in ADB, Barclays and GCB. Suppose ADB pays an interest of 2%, Barclays pays an interest of 4% and GCB pays an interest of 5% per annum and an amount of ¢350 more was invested in Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in Barclays is 2 times the amount invested in GCB.

a) Write down the three linear equations and represent them in the matrix form ?? = ?.

b) Find the amount of money Stonewall invested in ADB, Barclays and GCB using Matrix inversion.

A homogeneous system of linear equations has only the trivial solution.

True or false with full explanation