Let A = {a₁a2, a3} and B = {b₁,b₂, b3} be bases for V, and let P - equations is (are) satisfied by P for all x in V? OB) XB = PxA O Both A and B O None of A and B OAXA = PxB {[b1]A, [B2]A, [B3]A}

Q: solve all 132 q5

A: Step 1: Step 2: Step 3:Step 4:

Q: (c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the…

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Q: Given Å = £10 – ŷ + 22, B = -& + ŷ10 + 2 and Č = & + ŷ + 210. Vector (Ả x B) x Č is î10 + ŷ10 + 210…

A: To find  (A*B) *C from the given vectors.

Q: Both sets below are bases for P,: P = {pj, P2, P3} = {1+r?, 1+21, t + 21²} Q = {q,, 42» 93} = {1+3t…

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Q: Suppose a₁, A2, A3, a4, and a5 are vectors in R3³, A = (a₁ | ª₂ | a3 | 24 | 25), and 1 0 0 -5 0 1 0…

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Q: Given the vectors (1 10), (0 2 3), (1 2 3) in R3. Given vectors are linearly independent. Select…

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Q: The following limit lim Select one: O None of them 8x³y³ (z,y) →(1,2) 2x - y O equals 12. O equals…

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Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

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Q: 4. Prove that, for any vectors A, B and C, a necessary and sufficient condition that A x (B x C) =…

A: Given: Three vectors A,B, and C. To Prove: necessary and sufficient condition for A×B×C=A×B×C, is…

Q: 7. Let -3 6 -0--0-0-H [-] 8, V3 11 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are…

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Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

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Q: Let -3 ----------- V3 2 V1 = 6 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are in…

A: Let and

Q: If A is diagonalizable then A is diagonalizable. Select one: True False

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Q: Find w, where w3 = 1 + i. i? = -1.

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Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: Make z tu subject in the form of

A: Given x2a2-y2b2=1 Since we know that z=x+iy and z¯=x-iy then x=z+z¯2 and y=z-z¯2i

Q: Let a = (2, – 3, – 1) and b = (– 5, – 1, k). %3D %3D - Find k so that a and b will be orthogonal.…

A: Since we have been given that a⇀ = <2, -3, -1> and b⇀ = <-5, -1, k>Our aim is to find…

Q: Find the value of a for which U = a 1 10 is in the set 0 -1 3 0 H = span 5 3 -1 2 -2 -2 a =

A: The value of a=-7 .Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: 1. If A, B, and are any three vectors prove that À x (B x T) + B x (T × A) + T × (A × B) = ở.

A: If a, b, c are vectors then a×(b×c)=(a⋅c)b-(a⋅b)c  The dot property is p⋅q=q⋅p

Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

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Q: REMOVE vectors from Ac (P,[R], +,). To obtain a BASE for (P.[R],+,): of the items 25 and 26 (Item…

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Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

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Q: Let a = (1, – 5, 3) and b = ( – 5, 3, k). | Find k so that a and b will be orthogonal. k =

A: a→=1,-5,3b→=-5,3,k To find: value of k for which both will be orthogonal.

Q: Let u = , v = and w = . Now, i = is a linear combination of ü, v and w. That is, i = aju + azv +…

A: ANSWER:

Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

Q: If u = 2i + 5j; v = i - 2j; w = 3i - j, so u + v * w is:   -3   3   6 -6  9

A: Given that: u = 2i + 5jv = i - 2jw = 3i - j To find: u + vw

Q: Using index notation, prove the following identities among vectors A, B, C, and D: (a) (A x B). (B ×…

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 3.10. Rotate the vectors by 30%. *:[],三闾

A: We have to Rotate the given vectors by 30°.

Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

A: