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

A is 4×5 matrix with rank A =3.

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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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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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

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