3 1 4 -3 1 A = -2 -2 -5 -1 -5 -2 3 -1 Give a non-zero vector x in the null space of A. 2.

Q: {v1, v2, V3} is a linearly independent set of vectors in a vector space, then the subset {vı, v2} is…

A: Rule:-   If  a set of vectors in linearly independent in a vector space then , its subset is also…

Q: 1 -5 - 5 - 2 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine…

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Q: 3- The vectors x, = R3, are linearly independent. (1,0,1), x2 = (-1,0,1) and x3 = (-2,4, –3) in O…

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Q: 1 0 [-1 LetA = 10 2 140 -360 -1 170 1. Find the bases for col A and Row A. 2. Find a non-zero vector…

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Q: 1 2 0 0 3 1 -1 2. Express 14 as a linear combination of the columns of A = Then 2 0 0 1 find a…

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Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

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Q: 1 5 8 8 Let A : 3 4 4 4 2 5 6 1 6. 7 1. Rank(A) is Is / is not 2. Nullity(A) 1 3. The vector v = in…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Example S = {q1 = 2 + x + 4x², q2 = 1 - x + 3x², q3 = 3 + 2x + 5x²} a. Show that S is the basis for…

A: The given question is related with linear algebra. Given that,               S = q1 = 2 + x + 4x2 ,…

Q: 2. fu = and v = v1, v2, V3 > are two vectors in 3-space show k that u x v= u1 U2 U3 V1 V2 V3

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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: -9 -10 12 -15 A = 4 -8 6. Find a non-zero vector in the column space of A. 69

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Q: 月…- 2 Letting vi = 1 and vi = use Graham-Schmidt to find 0. orthonormal vectors (q1, q2}, and show…

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Q: a non-zero vector in the column space of A. A = -16 -4 0 -16 20 -20 -4 5 -5 20 0 25

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Q: 1 -1 -1 1 -1] Let A -1 -1 1 1 1 Find a non-zero vector x in the null space of A. -1 -1 -1 -1 X =

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Q: 7 -6 -5 -4 -3 -2 -1 -군 Find the vector shown above 3. 1. V

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Q: 1 -2 0 Find an explicit description of Nul A by listing vectors that span the null space.A =|0 -9 0

A: Consider the provided matrix A, We have to find an explicit description of Nul(A). The basis for the…

Q: 7. The set of vectors: [0 1 -3 -1], [1 0 1 11, (11-2, 0] is linearly independent. Answer: yes or no

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Q: (1.4) :(::)-(::) 3 4 3 4 %3D 2 2 2 2 Therefore Axiom 10 holds. Is this true or false? Give reasons…

A: This is the problem of vector space.

Q: 4. A vector is a linear combination if u can be written as a sum of scalar multiples of those…

A: We will use basic definitions and properties of Vectors and vector spaces

Q: х 1 0 -7 y 9 . If the kernel of A contains the vector 1 Let A = -2 what are x, y, and z? -1 4 z (х,…

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Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

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Q: -(:) --(:) --(1) --(3) 2 v2 = V3 = V4 = - 7 how that these vectors are linearly dependent. ind a…

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Q: [2 6 2 B = |4 6 0 -21 ; Determine a basis fot he column space of B. 2 L2 0 4

A: Given that, B=262-246022040 We need to find the basis for the column space of B.

Q: 1 -2 The vector b = -2 is in Span -1 3 1 -2 True False

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Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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Q: [2 4-2] 36 -3 1 2 16. Let A = Find a basis for the null space of A. What is nullity(A)?

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Q: Results for this submission Entered Answer Preview Result Message -5 -5-t In entry 3: Variable 't'…

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Q: Q. No. 3): (CLO-2, PLO-1) -1 1 180 – h Let A = 2 2h – 200 -360 -1 h 1. Find the bases for col A and…

A: We have to solve given problem:

Q: 1 a b Let A = 0 5 2 0 0 1 (i) Determine the condition of a and b so that A is diagonalisable.

A: Remark: An n*n matrix A is diagonalisable if and only if it has n linearly independent eigenvectors.…

Q: 2 3 2 2 Let A - 0 2 4 4 2 [1 2 2 2 3] 1. Rank(A) is 2 + 2. Nullity(A) 3 + 3. The vector v = 3…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: 15 8 8 6 3 4 4 4 Let A 1 2 5 6 6 7 1. Rank(A) is 2. Nullity(A) 3. The vector v = 1 + in the column…

A: Since you are asking multiple subparts. As per our guidelines, we are supposed to answer only the…

Q: basis of the null space A) {(-4,0, 1), (1, 1, 0)} 3) {(-4, 1, 1)}

A: we have to find a basis of null space of 14-128-2312-3

Q: 1.6 (Equality in Cauchy-Schwarz inequality). Prove that |(x, y)| = ||x|| · ||y|| if and only if one…

A: Image is attached with detailed solution.

Q: 0 1 4 0 10 Let A 1 1 2 2 Find a nonzero vector u in Nul(A).

A: As given matrix A=0014010-6-1122, We have to find a nonzero vector u→ for which Au→=0.

Q: (d) Show that Axiom 5 holds by producing an ordered pair- u such that u + (-u) = 0 for u = (u1, u2).…

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Q: 1 -4 -4 1-4 and b= - 10 If T is defined by T(x) = Ax, find a vector x whose image under T is b, and…

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Q: Given an n-vector x, no more than 6.25% of entries can satisfy | xi | ≥ 4 rms(x)

A: Lets try to think of a limiting case in which we try to minimize the rms. That will be achieve if i…

Q: (a) Suppose that a 120-vector a represents the age distribution of the customs in a bank, where a,…

A: (a.) Given: a is a 120-vector that represents the age distribution of the customs in a bank, where…

Q: х 3 Let A = -5 y 11 If the kernel of A contains the vector what are x, y, and z? -8 2 3 (х, у, 2)…

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Q: Find the stable vector of 1 P = | 0 1/2 1/4 01120 3/4

A: ANSWER:

Q: [i 5 -4 -3 17 -2 Find an explicit description of Nul A by listing vectors that span the null space.A…

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Q: 3 1 -1 Let A = 2 2 -1 Which of the following 4 -1 2 vectors satisfies Ax = 2x? (3) 1 2 1 V2 = , V3 2…

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Q: [4 4 1 -5 -1 A = 4. -1 1 -5 3 3. -1 3. Give a non-zero vector a in the null space of A. (Just any…

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Q: 1. A vector in the null space of A = 1 -2 -1 4 -3 7 -1 is: -8 1 -1 1 (b) 2. (a) (c) (d) -2 O d O b O…

A: First I have written a shor theory about null space of a matrix , just use them for given matrix and…

Q: -2 3 Question : Let A= 1 -3 -4 Find a vector x | -5 -5 Txi =Ax= b)rI -2 3 7-6 -3 -4 such that T(x) =…

A: Just solve the augmented matrix to get solution.

Q: -1 -1 1 -1 Let A = 1 -1 1 -1 1 Find a non-zero vector x in the null space of A. 1 1 1 1 1 x = -1

A: Here we find a nonzero element of null space of A

Q: 1 2 3 4 1. Let G and H be the points G (2, 9) and H (6, – 5). - 1a Find the vector HG in componerit-…

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Q: 1. a) Let x is n-vector and p and q are two constant n-vector. f(x) = ßx – q° - Ax – ql² is f(x)…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.