1. Let 1 2 -1 -2 -1 4 -2 -3 -1 10 -5 -3 -1 -3 -6 3 Find a basis of the null space and a basis of the column space of A.

Q: 7. Find a basis of the nullspace of 1 -3 -5 9 16 1 -3 -5 -2 B = -1 1 1 8. Find a basis of the column…

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Q: Find a basis for the nullspace of A. 6. 1 - 1 A=5 - 4 -4 7 -6 (a) 3 2

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Q: Find a basis for the null space and row space of A. 1 -1 3 A = 5 -4 -3 7 -6 3

A: Given: A=1-135-4-37-63

Q: Let Find an orthonormal basis of the row space of A. A = 1 4 1.[C ]]}.

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Q: Let 10 1-1 0 A = -2 1 0 1 -1 0 1 02-1 -1 Find a basis for the nullspace of A.

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Q: Let 9. A = 3 9 4 6. -3 2 -2 Find an orthonormal basis of the kernel of A.

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Q: Let -4 -6 4 6. A = 6. 2 -2 -6 Find an orthonormal basis of the kernel of A.

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Q: 4. A basis for R3 is Use Gram-Schmidt to find an orthogonal basis for the space.

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Q: (2) Find an orthonormal basis of ColA, where 3 -5 1 1 1 1 A = -1 -2 3 -7 8.

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Q: Let 1 1 -4 A = -3 9 -6 -2 8 -7 Find an orthonormal basis of the column space of A. 4 -18/5 -6 36/5

A: Consider the matrix A=[11-4-39-6-28-7]We find the basis for the…

Q: Find a basis for the null space of A -3 6 -1 1 -7 A = 1 -2 2 -1 2 -4 5 8 -4 3.

A: Given    A=-36-11-71-223-12-458-4We first find reduced row echelon form of  A.      Applying…

Q: Find a basis for the null space of A -3 -1 1 -7 A = 1 -2 2 3 -1 -4 5 8. -4

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Q: 1: Find a basis and determine the dimension of the following sub-spaces. H = { : 1a-c=0}. a b {:…

A: We have to find the basis and dimension of subspace

Q: 1. Find a basis of the null space of the matrix B = -2 -2 -4

A: See the attachment

Q: [1 1 Let A = 0 1 li o -2. 3 Find the rank and a basis for the column space of A.

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Q: | 1 1 2 3 4 3 5 3 14 7 ( 1 1. Find a basis for the null space of the matrix 1.

A: Dimension { (1;-2,1,0)}

Q: 3(b) Let x1, X2, ..., Xn be a basis for a vector space V. By generalizing the r produce an infinite…

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Q: Find the basis of the null space of A. 3 1 1 2 A = 4 1 2 1 1 –1 1 1 1 -1 [2 2 1 2 1 2

A: Step 1: Transform the matrix to the reduced row echelon form

Q: 1 10-200 001-300 If B= 0 0 00 10, then a basis for the column space of B is: 00 0 0 01 00 0 0 00

A: Given matrix is  B=110-200001-300000010000001000000 we have to find the basis for column space of B.

Q: 2. Find the basis for the nullspace of A, and the nullity and rank of A

A: This is a problem of linear transformation.

Q: 4. Let B = and observe that B is a basis for R³. Using the vectors in 3, find an orthogonal basis…

A: The solution are next step..

Q: Let 0 1 -1 0 1 A = -2 1 0 1 -1 1 0 2 -1 2 -1 Find a basis for the nullspace of A.

A: see below the answer

Q: Find a basis for the column space of B and a basis for the null space of B, -2 -1 1 1 -8 3 2 -4 -2…

A: Null Space: Null space of matrix A is given by N(A)=x∈V  Ax=0  where V is a vector space.Column…

Q: Find a basis for the null space of matrix A. 1 0 A = 0 1 0 0 0 -3 2 -1] %3D -5 3 A basis is -3 1

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Q: Let 1 5 A 3 3 -6 2 0 5 Find an orthonormal basis of the column space of A.

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Q: 4. A = 3 -6 -12 -3 -6 -9 -3 Find an orthonormal basis of the kernel of A.

A: Note: We know that the kernel of a matrix A is the set of solutions of the corresponding homogeneous…

Q: 3. Let 2 Wi = W = Span {wi, w2, W3}. W2 = W3 = Use the Gram-Schmidt process to find an orthogonal…

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

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Q: 2 1 Find an orthogonal basis for the column space of A = -1 -1

A: INTRODUCTION: If every pair of different vectors in a set is orthogonal, the set is termed an…

Q: Let -2 -1 -2 -6 -1 2 -2 A 1 -3 -7 -1 2 3 4 7 Find orthonormal bases of the kernel and image of A.…

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Q: Let [2 A = 3 4 2 1 -9 2 -6 nd an orthonormal basis of the kernel of A.

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Q: Let 1 0 1 1 0 1 A 1 1 0 0 1 1 find a basis for the column space of A; find a basis for Null space of…

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Q: 2. Find a basis for the null space and column space of the following matrix 1 3 1 3 0. 1 1 A = |-3 0…

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Q: 22 Find a basis for the null space of the following matrix [1 2 0 -1 3 1 -3 1 A = 1 2 2 4 1 1 -3 3…

A: Here the matrix given to us is  A=123110-1-3131202411-337 We have to find the nullity of the matrix…

Q: 8. Find a basis for the null space of 2 A = 2

A: As per guidelines we are  supposed to solve only first Question for second Question kindly ask it…

Q: 2 1. Find a basis of the null space of the matrix B -2 -2 -4

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Q: Let 1 -6 -2 A 1 -3 1 3 -8 4 Find an orthonormal basis of the column space of A.

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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: Find the following  1. basis for column space of A  2. a basis for the row space of A consisting of…

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Q: 12. Find a basis for the orthogonal complement of the row space of A: [1 0 2] A = 1 1 4 Split x =…

A: Orthogonal complement: Let W be a subspace of Rn. Its orthogonal complement is the subspace…

Q: If Col A has dimension 3, then the first three nonzero columns of A form a basis for Col A. True…

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Q: Let 1 -4 A = -2 2 6 3 10 Find an orthonormal basis of the column space of A.

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Q: Let Find an orthonormal basis of the column space of A. 2 5 3 -5 3 2 us

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Q: 1001 0 110 1-1 Find a basis of the row space of A= by reducing A to reduced echelon form. 1012 2…

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Q: 9 - - Let 1 3 5 A = -1 5 4 9 2 4 6 10 Which one is a basis for the column space, C(A), of A

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Q: 1 3 2 5 Find a basis for the Null Space and a basis for the Column Space of A 1 3 2 6

A: We have given a matrix 13251326 Now we wanna to reduce our matrix in row echelon form  for this C1 →…

Q: Let 3 A = 1 2 -8 2 Find an orthonormal basis of the row space of A.

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Q: |Let -2 1 -3 A 7 -1 Find an orthonormal basis of the row space of A.

A: Use Gram -Schmidt Orthogonalization process to find the orthonormal basis of the row space of A.

Q: 13. Determine whether or not the set {(1, -2, 3, 4), (–3, 2,5, –1), (–3, 2, 5, -3), (6, –4, 3, 0)}…

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Q: Find a basis for the null space of A = [³3 -3 1 2 -1 -2 4.

A: The given matrix: A=3121-3-1-2-1.We need to find a basis for the null space of A.

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.