Given a basis T = {[ 1 0 0 1 ] , [1 1 0 −1] , [0 0 1 1 ] , [0 0 −1 1 ]} for M2×2, (a) find [~v]T for ~v = [1 −1 7 4 ] (b) find ~u such that [~u]T = [−2 −1 3 0]

(1 2) 3. Let A = and B= 2 2 0 I. Compute tensor products A®B_and B® A ; II. Compute Hadamard products Ao B and BoA; III. Compute A•B' and (A®B)':

Find the coordinate vector of x = -5 with respect to the basis B = {| 7 1 for R3. 8 []B=

Compute the quadratic form x' Ax for A = X1 5 444 X2 -9 x3 a. x = a. x¹ Ax= b. x' Ax= C. X' Ax= 1/√√3 b. x= 7 C. X = - 1/√3 1/√√3 (Simplify your answer.) 360 643 035 (Simplify your answer.) and each of the following vectors.

-13/27] -4/27 -4/9 5/9 -20/27] -2/27 Let v₁ = √2 = and √3 = Find a vector in IR4 such that -20/27 ' ' -2/9 17/27 4/9 -2/3 2/9 {1, 2, 3, 4} is an orthonormal set. Answer:

Let the vector C represents the coefficients of a polynomial pt=c1+c2t+c3t2+c4t3. Express the conditions p0=1, p'0=2, p1=1, p'1=0 in the form AC=b.

(b) (c) 0 (69) (89-19) 0 0 0 0 (6 9.89.163) 0 0 0 0 2 1 0 0 2 4. Determine whether the following vectors are lin- early independent in 2×2: 0 (@) [9] [8