3 Are the following statements true or false??✓1. If the augmented matrix [A b] has a pivot position in every row, then the system Ax = b is inconsistent.2. The equation Ax = b is referred to as a vector equation.✓ 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x✓ 4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in IR™5. If the system Ax = b is inconsistent, then b is not in the column space of A.?6. If A is an m x 7 matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot have a pivotposition in every row.7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.?????

Answered: 3. Any linear combination of vectors…

Math

Algebra

3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 32E

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Question

Are the following statements true or false?
?
✓1. If the augmented matrix [A b] has a pivot position in every row, then the system Ax = b is inconsistent.
2. The equation Ax = b is referred to as a vector equation.
✓ 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x
✓ 4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in IR™
5. If the system Ax = b is inconsistent, then b is not in the column space of A.
?
6. If A is an m x 7 matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot have a pivot
position in every row.
7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.
?
?
?
?
?

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