Let 1 2 3 4 O A a. How many rows of A contain a pivot position? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work. Yes No [1 -2 0 1 0 0 2 2 0 4 0 0-2 -8 4 8 b. Does the equation A = have a solution for each b E R¹? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work. Yes No OO c. Do the columns of A span R4? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work.
Let 1 2 3 4 O A a. How many rows of A contain a pivot position? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work. Yes No [1 -2 0 1 0 0 2 2 0 4 0 0-2 -8 4 8 b. Does the equation A = have a solution for each b E R¹? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work. Yes No OO c. Do the columns of A span R4? Please note that, on an exam or quiz, you would be expected to defend your reasoning by showing your work.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
12
Transcribed Image Text:Let
1 2 3 4
000
A
Yes No
=
a. How many rows of A contain a pivot position? Please note that, on an exam or quiz, you
would be expected to defend your reasoning by showing your work.
1
0
0
4
Yes No
O
-2 0 1
0
2 2
0
0-2
8 4 8
b. Does the equation A = have a solution for each b € R4? Please note that, on an exam or
quiz, you would be expected to defend your reasoning by showing your work.
c. Do the columns of A span R4? Please note that, on an exam or quiz, you would be expected
to defend your reasoning by showing your work.
Expert Solution
Step 1
Given Matrix:
To find:
a) Number of rows has the pivot position.
b) whether the equation has a solution.
c) whether the rows of matrix span .
Concept used:
i) A leading one is the first nonzero entry in a row. The columns containing leading ones are the pivot columns.
ii) When the matrix of each row has the pivot element then it has a solution otherwise not.
iii) When a matrix having every column has a pivot element then it spans the space.
Step by step
Solved in 3 steps
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