A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A.3 331 2 8- 5A =6 5- 1 120 1 7- 62 2220 0 0Find a basis for Col A.(Simplify your answer. Use a comma to separate answers as needed.)

Remark: A basis for the column space ( the space that spanned by the column vectors) of a matrix A…

A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. 3 3 3 1 2 8 - 5 A = 6 5 - 1 12 0 1 7 -6 2 2 2 0 0 0 ... Find a basis for Col A. (Simplify your answer. Use a comma to separate answers as needed.)

A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. 3 3 3 1 2 8 - 5 A = 6 5 - 1 12 0 1 7 -6 2 2 2 0 0 0 ... Find a basis for Col A. (Simplify your answer. Use a comma to separate answers as needed.)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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Question

A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A.
3 3
3
1 2 8
- 5
A =
6 5
- 1 12
0 1 7
- 6
2 2
2
2
0 0 0
Find a basis for Col A.
(Simplify your answer. Use a comma to separate answers as needed.)

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Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).
In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector[w] ofwwith respect to the basis ={v1,v2}of 2or =v1,v2,v3 of3. v1=[101],v2=[121],v3=[111];w=[111]
Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..

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