2 0 -4 1 0 -2 -1 -41 0 -2 3 1 -4 4 -2 1 2 Given A = 1 -2 0 -3 -1 1 0 -2 0 -2 2- 1 0 -2 0 1 0 0 0 0 0 0 2 -2 1 1 (a) Find a basis for Col A. (b) Find a basis for Nul A. (c) What is dim Nul A? Explain. (d) What is rank A? Explain. 1. 1. 1.

Q: 2 -4 3 31 15. Given A = 4 10 -9 -7 8 -9 -2 7 find a basis for the column space of A. A is row 8 -2…

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Q: 1 -1 0 1] 1 3 1 -1 1 1 3. Let A = | 2 3 1 (a) Find an echelon form for A. (b) What is the rank of A?…

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Q: A) Find MS (B,C) B) Find a basis for the kernel of S C) Find a basis for the range of S D)…

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Q: 0 0 00 (a) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (c)…

A: Given A and B are row equivalent. The given problem can be evaluated as follows:

Q: -3 -8 6. (. 1 Let A = |2 1 5 -1 3 11 (a) (7 points) Find a basis for the rowspace of A. (b) (7…

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Q: 1 2 1 2 5 1 3 7 2 4 9 3 -1 A = 2 -2 4 1 0 0 1 -1 0 0 0 0 1 -2 3 0 -4 2 B = 0 0 0 0 (a) Find the rank…

A: As per the rules we can only able to solve the first three questions So i solved the first three.

Q: A 1 0 0 0 -6 9 1 2 0 0 0 00 (a) Find a basis for the column space of A. (b) Find the rank and…

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Q: 1 -3 2 0 1 0 1 -7 2 0 0 1 -3 0 1 -6 5 -7 4 3. You are given that A = 0 0 0 0 4 -12 7 7 2 3 -1 -7 1 0…

A:

Q: -2-5 BO-17 -5 1 A- -3-5 75-43 1 7 -13 S -3 01 -2 0 3 o o o 1-S Ca) Find the rank and nullity of A.…

A: Given matrix A is equivalent to matrix B so rank and nullity also same matrix A and matrix B

Q: 3 -1 0 -2 4 4 7 0 14 A = 4 4 0 8. -2 -4 0 -8 -2 (i) find a basis for the column space, (ii) find a…

A: Basis of columnspace is { ( 3, 4, 4, 2 ) , ( -1, 7, 4, -4 ) , ( 4, 3, 0, 2 ) }. Basis of rowspace is…

Q: 1 2 1 25 1 3 7 2 2 -2 4 9 3 -1 1 0 1. A = 4 3 0 -4 0 1 -1 0 2. B = 0 0 0 1 -2 0 0 00 0. (a) Find the…

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Q: 3 1 . A = 1 1 1 1 -2 -2 -2 0 -4 -2 (a) Determine rank A and dim Nul A and justify your answer. (b)…

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Q: 1 3 -7 - -1 A = -1 1 1 -1 1 -2 1 1 (a) Find a basis for Col(A). (b) Find a basis for Nul(A). (c)…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: A = B = 1 2 1 5 1 2 W N 0 0 1 0 2-2 3 7 11 25 8-1 8 10 30-4 0 1 -1 0 2 01-2 00 .00 00 0 (a) Find the…

A: As per the guidelines I am answering only first 3 parts. We have  A=12100251103722-211258-18 given…

Q: Question 2 In this question we are considering the vector space P2, which is the collection of all…

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Q: Find a basis for the column spac Find a basis for Col B where O [1 1 0 -2 0 0 1 4 0 0 0 0 0 0 0 0 10…

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Q: -2 -5 8 0 -17 1 3 -5 1 A = -7 -15 23 5 -77 1 7 -13 5 -3 1 0 10 1 0 1 -2 0 3 0 1 -5 (a) Find the rank…

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Q: 1 -2 -4 1 -2 1 -2 -4 1 -2 1 2 -3 -2 -3 0 1 -1 -3 -1 4. If A=1 -1 1 6. is row equivalent to B = 0 0 1…

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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: - 10 -7 0 0 - 10 3 7 2 10 2 3 An orthogonal basis for A, -6 -9 - 2 -2 is -6 - 3 7 Find the QR…

A: Given: A=-10-70025510-6-9-2-2161623232550 and q1=-102-6162, q2=33-303, q3=70770, q4=0500-5 is…

Q: -2 -2 1 -4 7 -3 -6 14 2 -6 -3 4 2 -2 -2 4 (a) a basis for the column space

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Q: Read and ansua Hhe Bilawng aneshans below ļi 1 find a basis for the saluhan sct of X-y+Zz-w= 0…

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Q: -2 -5 8 0 -17 1 -5 1 A = -5 -9 13 7 -67 1 -13 5 -3 1 0 1 0 1 0 1 -2 0 3 B = 0 0 0 1 -5 0 0 0 0 (a)…

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Q: (p, q) pq dx use Gram-Schmidt to find an orthonormal basis for P2[c], the space of all polynomials…

A: By using gram Schmidt process we solve the problem.

Q: 2 4 -3 -6- 14 7 -2 -4 -6 -3 1 -2 -2- 4 -2 Given (a) Find the rank and nullity of (b) Find a basis…

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Q: 1 3 -2 4 01 -9 -3 A = 3 6. 12 0 1 1 [ 4 8 o] -12 8 1. Find a basis for RS(A) 2. Find a basis for…

A: Matrix A is given.We find basis for RS(A),CS(A),PS(A). Note that  •Algorithm to find Bases for Row…

Q: 1 2 0 2 IV. Given A=-1 -6 3 -4 3 7 -1 6 Then (a) Find a basis for the row space of A ; (b) Find a…

A: Given that A=1202-1-63-437-16 (a) First it is required to find a basis for the row space of A. By a…

Q: 1. -3 -8 5 Let A = 2 1 5 3 5 -1 11 Find a basis for the rowspace of A. | Find a basis for the column…

A: We have to solve given problem:

Q: 5 . Evaluate L( -2 -1 3 . Find a basis for ker(L): } . Find a basis for im(L): }

A: Given that LX=12-38-2X.

Q: Let 4 -1 0 1 7 A = 13 -11 3 -1 -1 1 -3 13 -1 1 -3] Find orthonormal bases of the kernel and image of…

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Q: 1 2 -1 4 15. Find a basis for the null space of A. A=| 0 1 -2 3 (a) {(1,0, –1), (2, 1,0)} (с) (1, 2,…

A: The given matrix,  A=12-1401-23-10-32

Q: -1 5. Let v1 2 3 1 (a) Show that the set B= {ū1, 02, 03} is a basis for R³. (b) With B as in (a),…

A: The given question is related with vector space. Given that,                v1→ = 123 , v2→ = -121…

Q: 1 4 5 2 11. Given A= 2 1 3 0 -1 3 2 2 find a) the basis for colspace( A ). b) the basis for…

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Q: 20-211 0 0 0. 1 Q1 Let A = 20-20 0 0 1 a) Is A invertible? Justify your answer. b) Find a basis for…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: 3 -1 0 -2 4 7 14 3 A = 4 4 8 -2 -4 -8 -2 (i) find a basis for the column space, (ii) find a basis…

A: Given:  The given matrix is A=3-10-2447014344080-2-40-8-2

Q: -3 2 0 , В :).B = -2 2 -2 1 Let A = (, -1 -4 3 -4 5 -6 3 a) Find a basis for null(A). b) Find a…

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Q: 1 1 -1 1 -1 3 -1 2 -3 Let A= 4 -2 2 -3 -1 -2 -1 %3D 1 -2 1 1 1 -1 (take my word for it). 1 -1 The…

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Q: -4 2 A = -8 4 Find bases for the kernel and image of T(7) = AT. %3D { A basis for the kernel of A is…

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Q: 1 2 -1 -2 3 -4 Let A = -1 0 and i : 5 4 3 5 -4 1 Find a basis for col(A)+. Find projcol(a)a ī, i.e.,…

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Q: 1 -1 4 | 1 4 -2 (a) Let A = 1 Find an orthonormal basis of col(A). 4 2 -1 (b) Find an orthonormal…

A: First we need to find answer of part (a) to solve the part (b) question:-

Q: 1 10 0. 1 0. Given 2 -2 -1 4. 23 2579 234,

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Q: 6. Let A= | -| -4 | -2 -2 8 3 -13 || a) Find a basis fw Col A by Find a basis tur Nul A math 3326…

A: The solution is given as

Q: -2 4 01 -3 A = -9 6. 12 0 1 1 3 [-4 -12 8 8 0 1. Find a basis for RS(A) 2. Find a basis for CS(A) 3.…

A: As per the question we have to find the basis for the Row-Space, Column-Space & Null-Space for…

Q: 1-1 2 0) et A=2 -2 40 3 -3 7 0 Find a basis for the column space C(A). Y Find a basis for the null…

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Q: QUESTION -2 Let W = Span %3D -2 -7 3 8. 25 21 Find a basis for W.

A: W=span−2−2−28,−6−6−725,−6−6−321 To find a basis for W⊥

Q: [4 5 9 -21 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: 1 2 -2 76. 1 0 -2 3 01 2 2 -4 10 8 0 1 0 2 0 1.A= 0 1 0 2 2 =B 0 0 0 0 1 -2 2 4 -2 6 0 0 0 0 0 a. Is…

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Q: ( 1 Let A =(-2 -5 1 2 1). Find, b. 3 i. Find a basis for the null space of A. ii. Find a basis for…

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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.