14. Let u = 2 58 and A = 0 1 7 -J 0 . Is u in the subset of 2 13 R³ spanned by the columns of A? Why or why not?

Q: Find all (real) values of k for which A is diagonalizable

A: The algebraic multiplicity of an eigenvalue is the number of times the number appears as the…

Q: If B has a column of zeros, then so does BA if this product is defined. True O False 4

A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: Find two examples to demonstrate that if (a-d)2+4bc =0 then A may or may be diagonalizable

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Q: 1 0 0 0 2 500 A = 3 6 8 0 4 7 9 10

A: Find that columns of A are linearly independent

Q: Let A = 10-2 1 026 and b = 4 Denote the columns of A by a₁, a2, a3, and let -6 4 4 -6 W = Span {a1,…

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine whether w is in the column space of A, the null space of A, or both. 3 7 5 -6 3 1 A = 0 -4…

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Q: a= b= C= id=

A: As per the question we are given a two dimensional set V and we have to find the values of a, b, c,…

Q: Incorrectly, we usually say that when we multiply any number by ten we “add” a zero to the number.…

A: a) Jushua is wrong because the correct answer is 10×1.3=13 b) If a whole number is multiplied by 10…

Q: Linda planned to spend 9 hours practicing piano his week. By Tuesday, she had spent 2 1/2 hours…

A: Introduction: A fraction represents a portion of a total. This entire area can be considered a…

Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: Consider the vectors U₁ = 2x² + 2x - 1 and U₂ = -x² - 3x + 1 in P₂. Which of the following vectors…

A: Vectors v1=2x2+x-1 and v2=-x2-3x+1. To find the vectors that are linear combination of v1 and v2.

Q: Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} =…

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Q: Let 7 -7 2 -2 -5 %3D - 3 -2 9. -8 a) Find the dimension of the row space ofA. b) Find the dimension…

A: The given matrix,A=117-72-2-565-3-25409-8

Q: Determine whether b is in the column space of A. [-10 21 A = 5 8-10, b = 3 [-3-36 1. A

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Q: Let A = [1 2 3 5 4 6 7 8 Find the dimensions of Nul A, Col A and Row A.

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Q: Use the column-viewpoint to compute the product C = AB of [1 A = 1 = 1² 91 0 -17 1 2 and B

A: Given matrices:- A=1-11102 ,  B=201-1

Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

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Q: Q2. Let a vector A = [8-463] a) Compute the square of each element. b) Compute the square root of…

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Q: 10 - 2 7 Let A = 0 3 3 and b = 3 Denote the columns of A by a,, a2, ag, and let W = Span (a,, a2,…

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Q: 1. Determine whether b is in the column space of A, and if so, express b as a linear combination of…

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Q: 2. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

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Q: Verify that (AB)T = BTAT.

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Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

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Q: Let A = {1, 2, 3} and B = {1, 3, 5}. Let A × B denote the Cartesian product of A and B. Indicate if…

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Q: Compute u – 3v, u v and u x w.

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Q: 12. Find bases for the row space and column space of A. 1 4 9 22 2 7 16 A = 6-3 3

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Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: 6. Can any of the given sets of 3-vectors below span the 3-space? Why or why not? (a) [1 2 1] [231]…

A: We have to check whether the given set of 3-vectors span the 3 space. (a) 1 2 1, 2 3 1, 3 4 2 (b) 8…

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: 123 2 3 5 is all vectors e column space of A 246 bi b 3= by ER such that by O a. by= by Ob. 2by b…

A: