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• ### Let ?: ?2(R) ⟶ R3 be a linear transformation such that ?(1) = (−1, 2, −3),...

Let ?: ?2(R) ⟶ R3 be a linear transformation such that ?(1) = (−1, 2, −3), ?(1 + 3?) = (4, −5, 6), and ?(1 + ?2) = (−7, 8, −9). a. Show that {1,1 + 3? ,1 + ?2} is a basis for ??2(R) (7pts) b. Compute ?(−1 + 4? + 2?2). (3pts)

• ### Let V P2(R) and let T V-V be a linear transformation defined by T(p)-q, where (x)(r...

Let V P2(R) and let T V-V be a linear transformation defined by T(p)-q, where (x)(r p (r Let B = {x, 1 + x2, 2x-1} be a basis of V. Compute [TIB,B, and deduce if it is eigenvectors basis of

• ### Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0)...

Let T: R3 - R be a linear transformation such that T(1,1,1)= (2,0,-1) T(0,-1,2)=(-3,2,-1) T(1,0,1)= (1,1,0) Find T (2,-1,1). a) (10,0,2) b) (3,-2-1) c)(2,2,2) d) (-3,-2, -3)

• ### Let T: P2 + P, be a linear transformation for which T(1) = 3 - 2x,...

Let T: P2 + P, be a linear transformation for which T(1) = 3 - 2x, 7(x) = 9x – x2, and 7(x2) = 2 + 2x2. Find T(2 + x - 8x?) and T(a + bx + cx?). T(2 + x - 8x2) T(a + bx + cx) II

• ### 2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2...

2) Let T be a linear transformation from P3(R) to M22(R). Let B= (1+2x + 4x2 + 8x3), (1 + 3x + 5x2 + 10x3), (1 + 4x + 7x2 + 13r%),(1 + 4x + 7x2 + 14x²). Let C= [] [ 1];[1 ] [ ] 0 17 40 Let M= 13 31 36 124 22 52 -61 -209 23 55 -64 -220 be the matrix transformation of T from basis B to C. -47 -161 The closed form of...

• ### could u help me for this question?thanku!! 21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x...

could u help me for this question?thanku!! 21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T. 21. Let T...

• ### 2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2]...

2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)

• ### QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and...

QUESTION 4 Let T R3-P2 be defined by T(a, b, c) - (a + b + e) +(a+b)a2 (4.1) Show that T is a linear transformation (4.2) Fınd the matrix representation [T]s, B, of T relative to the basıs in R3 and the basis in P2, ordered from left to right Determine the range R(T of T Is T onto? In other words, is it true that R(T)P2 Let x, y E R3 Show that x-y ker(T) f and only...

• ### Let T: R3 ? R3 be a linear transformation such that T(1, o, o)-(4,-1,2). TO, 1,...

Let T: R3 ? R3 be a linear transformation such that T(1, o, o)-(4,-1,2). TO, 1, o)-(,-2. 3), and To, o. 1)-a,-20·Find the indicated image.

• ### Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that...

Let T:P2 P2 be the linear transformation defined by T(p(x)) = p(4x + 5) - that is T(CO + C1x + c2x2) = co+C1(4x + 5) + c2(4x + 5)2. Find [7]3 with respect to the basis B = {1, x, x?}. Enter the second row of the matrix [7]z into the answer box below. i.e.. if A = [7]B. then enter the values a21, a22, 223, (in that order), separated with commas.