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A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true for A. There exists a rank two matrix B such that AB os a zero matrix

A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true for A. There exists a rank two matrix B such that AB os a zero matrix

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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Question
A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true for A. There exists a rank two matrix B such that AB os a zero matrix O For every vector b in R^4 the matrix equation Ax - b has infinitely many solutions O For every vector b in R^4 the matrix equation Ax = b has a unique solution O There are vectors b in R^4 such that the matrix equation Ax = b has no solution. However, if Ax = b$ has a solution then it is unique
Transcribed Image Text:A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true for A. There exists a rank two matrix B such that AB os a zero matrix O For every vector b in R^4 the matrix equation Ax - b has infinitely many solutions O For every vector b in R^4 the matrix equation Ax = b has a unique solution O There are vectors b in R^4 such that the matrix equation Ax = b has no solution. However, if Ax = b$ has a solution then it is unique
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