Consider the multiplication operator LA: R2 R2 defined by LA(z)= Ax where A = E is the standard basis. -8- b₁ = .b₂ = . Find an ordered basis B = (b1,b₂) for R² such that [LA] = 37 15 -96-39 Hint: [LA] A where

Q: Explain why S is not a basis for P2. S = {1, 4x, -6 + x², 7x} O sis linearly dependent. O s does not…

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A: (.) Note: '' As per guidelines we will solve first three subparts. If you want any specific subpart…

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Q: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

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Q: Consider the bases for M2x2(R) given by a' : and a the stan- dard basis. For the transformation T :…

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Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: 2 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have…

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Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: please explain part d because i am confused by the second and third part of part d.

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Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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Q: -10 [x] B = 10 -10 25/24 2,0 -35/24 Find the coordinates of x in the ordered basis B = (a, b). 2,0…

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Q: Let TA:R³ R³ be multiplication by -150 A = 2 1 2 6 7-5 and let e₁,e₂, and e3 be the standard basis…

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Q: Explain why S is not a basis for R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

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Q: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

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Q: The vectors : 1 3 5 2 = = 11 --8-8-6 = 0 7 form a basis for R³ if and only if k k

A: Given vectors form basis for R^3 iff when k=21.Explanation:Three vectors from R3 from basis for  R3…