Let M = {[; 1-C %3D Then M is a basis for

Q: Which of the following is the standard basis of M22? 0. 0. 0. Lo o][1 o]* o 0. 0 1] 0 0 1.

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Q: Which of the followings is a basis for P3: a) {x³, x², x³ + x2,x} b) {x³, x(x + 1), 1} c) {x³, x³ +…

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Q: Explain why S is not a basis for R2.S = {(2, 3), (6, 9)}

A: We know the basis of R2 = {(1,0),(0,1)} So it has 2 elements So, another basis of R2 also must have…

Q: Let S then S is a basis for R C

A: S = ( 12, -1c ) So set S to be a basis of a given vector space the vectors should be linearly…

Q: In Rª, let S = {(1,2,2, –1), (0, –1,4, 2)} and T = U = sp(S) and W = sp(T). Find a basis for U +W…

A: Your approach is absolutely right!

Q: Is the set S = {(0, 0, 6), (1, 5, 3), (0, 1, 2)} a BASIS for R? %3D a. yes C. either b.no d.…

A: If V is a vector space over F and v1, v2,... vn then these n vectors are said to be linearly…

Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

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Q: Let S = {(a, b, c, d) | a, b, c, d ɛ R, a = c, d = a + b}. Find a basis for S.

A: Given that a=c So they are the same element, so we can ignore c

Q: Let M = {(, Then M is a basis for M3,2 O None of the mentioned O the above M2,3 the above

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Q: Every basis for R4 contains

A: Every basis of ℝ4 contains ______________

Q: Explain why S is not a basis for M22

A: We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Q: Explain why S is not a basis for P2.S = {−1, 11x}

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Q: Find a basis for the null space of the matrix. [10-7-4] 6) A = 01 5-2 [00 0 o] D) 明“

A: We have to find the basis for the null space of the matrix A.         According to our guidelines we…

Q: 15 tig = 12 0. 6. form a basis for R if and only if k #

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Q: Is the set S = ((0, 0, 6), (1, 5, 3), (0, 1, 2)} a BASIS for R? c, either a. yes b.no d.…

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Q: Let M = {(, ¿ )-G i )G : DC : D Then M is a basis for M2,3 the above M3,2 the above O None of the…

A: Given that     M=110000, 110010, 100101, 100001

Q: Let M = { : 9-6 ¿ 6:9C: 9C : } Then M is a basis for None of the mentioned M2,3 O the above M3,2 O…

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Q: 16. Determine whether the given set forms a basis for P3. {-1 -r', 2r + 2r", –2r + r – a*, 1+ r² +…

A: Follow the steps.

Q: Determine whether S is a basis for M2,2. 2 01 2 0] [o 2 0 1 0 5 4 2 4 1 2 0 O sis a basis of M2,2- O…

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Q: Find a basis for the null space of the matrix: [1 A = -1 -1 1 4

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Q: O Is the sed 5-[2],[2 1]" basis for R".

A: A basis is linearly independent and spans the space   We are allow to solve first question only. If…

Q: (b) Calculate a basis C for S and state dim(S).

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Q: Find a basis for the null space of matrix A. 17 1 0 -4 3 A =0 1 3 0 0 0 1 4 0.

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Q: Determine whether S is a basis for M2,2.

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Q: Find a basis for the null space of the matrix. A = C C [10-40-4] 01 20 2 00 01 1 100 00 0 42100 0 0…

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Q: Find a basis for N(A) and give the nullity and the rank of A. -1 2 0 A 2 -5 1

A: Suppose A is any mxn matrix then RankA+NullityA=n

Q: Show that the set below is a basis for R3. S = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}

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Q: Find the nullity, rank and a basis for the null space of the matrix A, where (1 3 3 A =| 2 4 -4 1 1

A: first we will find the reduced row Echelon form of the given matrix (rref(A)). Rank of A is number…

Q: 2. Determine whether the set S = {(2, 0, 1), (2, -1, 1), (4, 2, 0), (-6, 2, 3)} a. Spans R3 b. Is…

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Q: Determine whether S is a basis for P3.S = {−1 + t3, 2t2, 3 + t, 5 + 2t + 2t2 + t3}

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Q: Let O 0 10 -1 A = |0 0 0 1 3 1 4 0 0 A basis for Null(A) is given by:

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Q: Г1 2 0 1 2 4 1 - A = 3 6 -1 8 4 8 -1 12 8

A: Given matrix is A=1203124−15436−18548−1128. We have to find a basis for the null space of the matrix…

Q: • MMD7;10 Let M = Then M is a basis for M2,3 O the above M3,2 the above None of the mentioned

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Q: Determine whether S is a basis for M2.2. -{::}| 2 0 2 0 0 1 0 1 S = 0 5 5 1 3 2 2 0 O sis a basis of…

A: Since given set is finite if it is linearly independent then S is basis. Show that S is linearly…

Q: c) Find a subset of S that is a basis for W.

A: A linearly independent set of vectors is a basis of a subspace W if it spans W. Now since S spans W,…

Q: Let S = {2x, 1 -x,x² + x - 1,x + 1,x – 2}. Then None of these P2 S is a basis for the above P.

A: S is said to be basis of R3 if S is linearly independent L(S) = R3

Q: The following set S of matrices spans M22. Find a subset BCS that is a basis for M2.2. 3 S = 3 2 0 9…

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Q: 2) Determine whether S = {(0,3,-2), (4,0,3)(-8,15, -16)} is a basis for R3.

A: Given that, S=(0,3,-2),(4,0,3),(-8,15,-16)

Q: Determine whether S is a basis for P3. S = {3 – 2t2 + t3, -2 + t², 3t + t³, 5t} S is a basis of P3.…

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Q: Find a basis for (null(B))+, where 1 2 -1 -3 2 2 4 -2 1 4 B := 1 2 3 -1 -2 1 2 11 -11 -10

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Q: 12. The et 5 - {; 96 1A}- is: a. a basis of M22- b. not a basis of M2,2.

A: The standard basis of M2,2 is: e1=1000 ,   e2=0100 ,     e3=0010 ,    e4=0001

Q: Determine whether S is a basis for P3. S = {2 – t, t³, 7², 8t + t³, -1 + 2t} S is a basis of P3. S…

A: It is to be checked whether S is a basis of P3 or not where  S=2-t, t3, 7t2, 8t+t3, -1+2t

Q: Given that B = { [1 -2 3], [0 1 0), [0 2 1]} is a basis of R and C = {[-3 -5 6], [2 3 -3], {[- 3 [0…

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Q: 1. Explain whether S = {1, 2x, x² – 4, 5x} is a basis for P2 or not.

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Q: Find a basis for the null space of each given matrix A 1 -1 2 1 | 2 1 -1 3 12. A = | 5 -1 3 3 4 -2 5…

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

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

A: The set is S=1000,0110,1001,8-4-43   Known fact: A set of vectors S=v1,v2,…vn is a linearly…

Q: Determine whether or not S = {x² +1, x+ 2, –x² +x} is a basis for P2.

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Q: Let Find a basis for the null space of A. A = -2 3-1 -6 9 -3 33

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Q: The following set S of matrices spans M2 2. Find a subset BCS that is a basis for M2 2. 1 1 1 1 1 -1…

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Q: Solve using the concept of rank.

A: We write the matrix representation of S to get the answer. Recall that B=1000,0100,0010,0001 is a…