2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0 and let a1,. , as € R® be the columns of A (in left-to-right order). (a) necessary to bring it to this form. Which row operation is it? (Do not rewrite the entire matrix; just describe, in words or symbols, the row operation.) The matrix A is not in reduced echelon form, but only one elementary row operation is (b) Does a, belong to the span of a1, a2, az, a4, az, and ag? If not, explain why not; if so, write az explicitly as a linear combination of these six vectors. (c) Exactly one of the following three sets of vectors is linearly dependent: {a1, a3, a4, as}, {a1, a3, a5, a7}, {a1, a3, a4, a5}. Identify which one it is, and find an explicit linear dependence relation among the vectors in it.
2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0 and let a1,. , as € R® be the columns of A (in left-to-right order). (a) necessary to bring it to this form. Which row operation is it? (Do not rewrite the entire matrix; just describe, in words or symbols, the row operation.) The matrix A is not in reduced echelon form, but only one elementary row operation is (b) Does a, belong to the span of a1, a2, az, a4, az, and ag? If not, explain why not; if so, write az explicitly as a linear combination of these six vectors. (c) Exactly one of the following three sets of vectors is linearly dependent: {a1, a3, a4, as}, {a1, a3, a5, a7}, {a1, a3, a4, a5}. Identify which one it is, and find an explicit linear dependence relation among the vectors in it.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2.
Consider the 6 x 8 matrix
[1 3 0 0
0 0 1 0
2 0 5
-3
0 0 0
A
0 0
1
4
-7
-9
00
0 0 0 0
0 0 0 0
0 0
and let a1,.
, as € R® be the columns of A (in left-to-right order).
(a)
necessary to bring it to this form. Which row operation is it? (Do not rewrite the entire matrix; just
describe, in words or symbols, the row operation.)
The matrix A is not in reduced echelon form, but only one elementary row operation is
(b)
Does a, belong to the span of a1, a2, az, a4, az, and ag? If not, explain why not; if so, write
az explicitly as a linear combination of these six vectors.
(c)
Exactly one of the following three sets of vectors is linearly dependent:
{a1, a3, a4, as}, {a1, a3, a5, a7}, {a1, a3, a4, a5}.
Identify which one it is, and find an explicit linear dependence relation among the vectors in it.
(d)
Determine dim Col A and dim Nul A.
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