Determine whether S is a basis for M₂ ¹2,2 20 25 [21 02 --{[39]- [32] [33] [23])}) = ² | S 05 02 30 Os is a basis of M2,2" Os is not a basis of M2,2-

Q: Let Is S a basis for R³?

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Q: Given that the set (1, 1+x+x,p(x)} is a basis for AX = P,, which of the following is a possible…

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Q: Let M1 M2 M3 = and 3 4 A1 = A2 A3 : Let B {M1, M2, M3} and W = span(B). It can be shown that B' {A1,…

A: The solution is given as follows

Q: 7) Is the basis B = an orthonormal basis? If it's not, then can we make it to become one?

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Q: 5) B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates…

A: A change of basis consists of converting every assertion expressed in terms of coordinates relative…

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: 25. B = (f1, f2, f3) is a basis for R2[x] where fi = 1+ x + 2x², f2 = 1 + 2x + 5x², f3 = 2 + x +…

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Q: If a, b, c are given with a -/=- 0, how would you choose d so that [ � �] has rank 1? Find a basis…

A: To have rank 1, given that the first row is non-zero, the second row should be a multiple of the…

Q: (16v2,2v2) is any B = {(, -),,)} be an orthonormal basis for R. If Let vector in R, determine the…

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Q: G #2 Find the minded parmamial H ne legenvecters basis L 2 fie geneanzen

A: Given : A=-311-622-311 To Find : Minimal polynomial

Q: Is the set S=I21",[ - 1 31], [2 4 5 ]] [-1 -1 3 1 a basis tor R".

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Q: 12. Let S = span {(-)-(- -)} (a) -{0-0-6)} (b) 5 (c) ~ {(-9)-(-)} {(-9)} •{(-)-(-)-()} -{(G)-()} 3 4…

A: For finding the basis we have to find the row space of vector that span S

Q: 33. Suppose V is known to have dimension k. Prove that (a) any k independent vectors in V form a…

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Q: Let s= {(1,3.5). (3. 3, 2). (-1, 1.8)} be a basis for R. If u = (8, 8, 1), then (u), - A) (1 2 1 B)…

A: The solution is given as

Q: 10. (a) Define: Basis 6 -1 -2 2 3 -4 5 8 (c) Find dim(nul(B)) and dim(col(B)), does your result…

A: The given matrix B=-36-11-11-223-12-458-4. We have find a basis for the null space of B and the…

Q: 0 1 0 S = {(1 3)·(¦¯¯^¹)· (² ¦ ). ( -º2³)} 03 4 0 23 2 is independent or not and if it is not,…

A: Recall the definition of linear independence i.e non-zero span of vectors must be non-zero. If a…

Q: Which set is an orthogonal basis containing ã = (5,12) ? { (5,12),(5,–12) } { (5,12),(5,12)} {…

A: Option (d) is the orthogonal basis which containing the vector (5,12).

Q: Which one of the following is an orthonormal basis of R³? 1 {]--]} {B}. √3 √2 3 {]···]} √2 2 √6 0 /6…

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Q: [4 5 9 -2 1. Consider A = 6 5 1 3 4 8 -3 12 (a) What is Nul A? (b) Find a basis for Nul A. (c) What…

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Q: 2 -3" A = 2 –1 4 4 3 -2

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Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: 9. Let S = { (1,2), (4, 5), (0, 2)}. Check whether S is a basis for ?2?

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Q: 3. Prove whether { 221 2} is or is not a basis for R³. Be sure to discuss the requirements in the…

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Q: Suppose S={1+ 3z , 1-4x*}. wh.ch of the pollynomiais given Could be added to the set S to form basis…

A: We know that any 3 Linearly Independent vectors form a basis for P2 . Hence we have to check whether…

Q: 10 - Which set is an orthogonal basis containing å = (3,4) ? { (3,4),(-3,4)} mo { (3,4),(-4,3) } {…

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Q: Let }].,)} 3 B = { 1.E be basis for IR %3D 2 Is B orthonormal ? False True

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Q: Jump to level 1 Given the ordered basis 5 B=A₁ = = {4₁ - [573].4₂2 - [69]. -7-9 [8 A3 = 5,3], 2-3 A4…

A: Assume coordinated of A with respect to B is Hence

Q: 4. Find a basis for the span of {[1, 2, 1]" , [3, 1, –1]", [1, –3, –3]"}

A: Given: uvw = 121, 31-1, 1-3-3 To find: The basis for the span. Concept Used: To find a basis for the…

Q: = 6 | [1 0 , E12 Eu = 8 En = 8 . and En = 7. Let E11 and E22 Use the {E11, E12, E21, E22} is a basis…

A: That's easy. Have a great day!!!

Q: This graph represents the function f (x) = x² – 2x + 2. %3D -

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Q: [4 5 9-21 1. Consider A = 6 5 1 12 3 4 8 -3 (a) What is Nul A? (b) Find a basis for Nul A. (c) What…

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Q: Find a basis for Q(√2, √6 + √10) over Q(√3+ √5).

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Q: 7. Let B = {(1,2,3), (2,0, 4), (1, 1, 1)}. Prove that B is a basis for R³ (since this is a proof,…

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Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…