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-1 1 -2 4 8 -1 Consider the following matrix A = -2 -3 13 2 -1 4 -1 -11 3 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2).

-1 1 -2 4 8 -1 Consider the following matrix A = -2 -3 13 2 -1 4 -1 -11 3 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2).

Advanced Engineering Mathematics
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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-1 1 -2 4 8 -1 Consider the following matrix A =| 2 -2 -3 13 2 -1 4 -1 -11 3 5 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2). 4. Find a basis for Null(A). -5 5. Find the value of k such that the vector b = 3 is in Null(A). 1 6. What is the rank of A and the nullity of A? -2 000 8 -2 7. Is the set of vectors { 4 13 linearly dependent or indepen- -1 -11 6. 16 dent? Justify.
Transcribed Image Text:-1 1 -2 4 8 -1 Consider the following matrix A =| 2 -2 -3 13 2 -1 4 -1 -11 3 5 16 1. Find a basis for Row(A). 1 2. Find a basis for Col(A). 8 13 3. Write the column as a linear combination of the basis vectors se- -11 16 lected in 2). 4. Find a basis for Null(A). -5 5. Find the value of k such that the vector b = 3 is in Null(A). 1 6. What is the rank of A and the nullity of A? -2 000 8 -2 7. Is the set of vectors { 4 13 linearly dependent or indepen- -1 -11 6. 16 dent? Justify.
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