4-1) describe the possible echelon forms of the matrix. (a) A is a 3x3 matrix with linearly independent columns. (b) A is a 4x3 matrix, A=(a, a, a), such that (a.. a.) is linearly independent and a, is not in Span (a, a).
4-1) describe the possible echelon forms of the matrix. (a) A is a 3x3 matrix with linearly independent columns. (b) A is a 4x3 matrix, A=(a, a, a), such that (a.. a.) is linearly independent and a, is not in Span (a, a).
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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Question
![4-1) describe the possible echelon forms of the matrix.
(a) A is a 3x3 matrix with linearly independent columns.
(b) A is a 4x3 matrix, A=[a; az as], such that (a₁. a) is linearly independent and as is not in
Span (a₁, az).
4-2)
(a) How many pivot columns must a 7x5 matrix have if its columns are linearly independent? Why?
(b) How many pivot columns must a 5x7 matrix have if its columns span R³? Why?
(c) Fill in the blank in the following statement: "If A is an mxn matrix, then the columns of A are
linearly independent if and only if A has ( ) pivot columns." And explain why the statement is
true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37523b4-8106-408f-9300-625624498825%2F660cb7ed-54c1-4240-8b91-ffd1c776c975%2Fk2f3xlv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4-1) describe the possible echelon forms of the matrix.
(a) A is a 3x3 matrix with linearly independent columns.
(b) A is a 4x3 matrix, A=[a; az as], such that (a₁. a) is linearly independent and as is not in
Span (a₁, az).
4-2)
(a) How many pivot columns must a 7x5 matrix have if its columns are linearly independent? Why?
(b) How many pivot columns must a 5x7 matrix have if its columns span R³? Why?
(c) Fill in the blank in the following statement: "If A is an mxn matrix, then the columns of A are
linearly independent if and only if A has ( ) pivot columns." And explain why the statement is
true.
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4-1) Here, to describe the possible echelon forms of the matrix.
a) A is a 3x3 matrix with linearly independent columns.
b) A is a 4x3 matrix, A=[a1 a2 a3], such that {a1,a2} is linearly independent and a3 is not in Span {a1, a2}.
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