Quest In P₂, let B and C be the bases where B = {1-312, 2+t-5t2, 1+2t) and the standard basis C = {1, t, t2}. Find the coordinates of x=t² O O C NO O 123 0 1 2 17 0 12 [-3 -5 0] 321 H 1 0 0[³] 2 11 12

Q: 3. Let A = a. b. 1-2 3 1 1 1 Find the Null space of A. Find a basis for Null space of A. c. Find the…

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Q: 2 Consider the bases B₁ and B₂. 2 -3 -7 4 {{³][])} {₁ 6 -5 B₁ = Find [x]B₂ if [x]B₁ 2 [²]. 6

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Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: isider the complex number 3 a = 4+i√2, where i² = -1. (a) Find the minimal polynomial of a over Q.…

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Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (–2, –1,2), (4,2, –4)} for R³ b) S = {2,2,x +…

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Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: The vectors -4 THELB 2 and V3 = -4 form a basis for R³ if and only if k +- VI 7 -6 0 V2 13 -14 k

A: The vectors v1=7-60, v2=-42-4,  and v3=13-14kform a basis for R3 if and only if k≠?.

Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Using the scalar form of the table 1 3 2 3 1 1- - a 1 6 = 6+ a 5 4-a 2 -2 5 12 19 to determine the…

A: Step 1: Write the matrix A in scalar form. A = [[1, 3, 5, 6 + a], [2, 3, 4 - a, 2], [1, 1 - a, - 2,…

Q: Determine whether the set of polynomials 10. i (I+ x2, x + X2, 2 t x} is a basis forr Pe (TR).

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Q: 0. The vectors 2 0 , and 1 form a basis ofR. 3 3 a) True b) False

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Q: 1 Which of the following is a basis of R4that includes the vectors and 1 ? 1 -1 1 1 1 1 1 1 -1 1 1 1…

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Q: 1 3 -2 4 Find the row space and null space of A = -1 2 . Write each as the span of a basis. -6 4 -8]…

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Q: - Determine if S = {[1246]} 0 forms a basis for M2,2.

A: We know that M2×2 is a vector space of all 2×2 real matrices over R.Given that .We need to determine…

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: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Given that

Q: - 10 -8 2 4 -6-8 16 2 of A with the given orthogonal basis. 6 1 4 11 6-3 16 30 23 4 4 1 An…

A: We have to find the  factorization of the matrix

Q: –10 S = l2] ] 13 2. 2.

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Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

A: Given H=3a+6b−c6a−2b−2c−9a+5b+3c−3a+b+c:a,b,c∈R We have to find the basis for H. First write the…

Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: 7) The vectors. A) True 13 False 17 -19 + -34 38 17 2 form a basis for n

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Q: Which one of the following is an orthonormal basis of R³? {Q.0·0} 1 1 امام امامت امام 0 3 0 L √2 0…

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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: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

A: Given that x=(1,1) and y=(5,-1)

Q: 41 1 -1 -8- 1 3. -2 Find the basis for the column space of -2 -6 4 a. {0 C. a 3. b. { d. {-1

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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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…

A: Since  in the usual basis  has coordinates, . So, to obtain its coordinates in the basis,  , where

Q: Let [3³] Ai B , where B = {b₁,b₂} is a basis in R². Then 3 B 061+06₂

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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…

A: In n-dimensional Euclidean space (often denoted as ℝ^n), the standard basis consists of n vectors,…

Q: Given the ordered basis B=A₁ -1 0 -[5], 42 - [8 A₂ -2 6 (4]} 8 16 -33 -1 3 [¹].4 A4 0 -9 A3 - find…

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Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

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Q: ,B = the standard basis, C - {[; -}-[; :)-8)-[: 9]} in 22 (a) Find the coordinate vectors [A] and…

A: The standard basis B for M22 is {e1,e2,e3,e4}.

Q: -10000- Show that the set spans R. Find a subset of these vectors that is a basis 3 2 3 for R3. 2.

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