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Let a₁, a2, a5 denote the columns of the matrix A shown to the right and let B =[a₁ ª₂ 84 ] Answer parts (a) through (c) below. A = ليا 3 2 6 -3 1 2-18 4 39 3-9 -2 4 76 3-6 -1-3 72 a. Explain why a3 and as are in the column space of B. Choose the correct answer below. A. The column space of B is all of R4. OB. The pivot columns can always be written as a linear combination of the free variable columns. OC. The systems Bx=a3 and Bx=a5 are both inconsistent. OD. The reduced echelon forms for [B a3] and [B a5] are the same.

Let a₁, a2, a5 denote the columns of the matrix A shown to the right and let B =[a₁ ª₂ 84 ] Answer parts (a) through (c) below. A = ليا 3 2 6 -3 1 2-18 4 39 3-9 -2 4 76 3-6 -1-3 72 a. Explain why a3 and as are in the column space of B. Choose the correct answer below. A. The column space of B is all of R4. OB. The pivot columns can always be written as a linear combination of the free variable columns. OC. The systems Bx=a3 and Bx=a5 are both inconsistent. OD. The reduced echelon forms for [B a3] and [B a5] are the same.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let a₁, a2...., a5 denote the columns of the matrix A shown to the right and let B =[a₁ 32 34 4] Answer parts (a) through (c) below. A= 3 3 6 - 3 2 1 2 18 4 39 4 76 72 3-9-2 3 -6 -1 - 3 - a. Explain why a3 and as are in the column space of B. Choose the correct answer below. O A. The column space of B is all of R4. B. The pivot columns can always be written as a linear combination of the free variable columns. C. The systems Bx=a3 and Bx=a5 are both inconsistent. D. The reduced echelon forms for [B a3] and [B a5] are the same. E. The free variable columns can always be written as a linear combination of the pivot columns. b. Find a set of vectors that spans Nul A. A spanning set for Nul A is
Transcribed Image Text:Let a₁, a2...., a5 denote the columns of the matrix A shown to the right and let B =[a₁ 32 34 4] Answer parts (a) through (c) below. A= 3 3 6 - 3 2 1 2 18 4 39 4 76 72 3-9-2 3 -6 -1 - 3 - a. Explain why a3 and as are in the column space of B. Choose the correct answer below. O A. The column space of B is all of R4. B. The pivot columns can always be written as a linear combination of the free variable columns. C. The systems Bx=a3 and Bx=a5 are both inconsistent. D. The reduced echelon forms for [B a3] and [B a5] are the same. E. The free variable columns can always be written as a linear combination of the pivot columns. b. Find a set of vectors that spans Nul A. A spanning set for Nul A is
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A=\begin{pmatrix}3&3&2&2&-18\\ 6&-3&1&4&39\\ 3&-9&-2&4&76\\ 3&-6&-1&-3&72\end{pmatrix}

part(a) is absolutely correct

now convert the above matrix into a reduced row echelon form

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