**Example 7:** Find (a) the rank and nullity of \( A \) and (b) a subset of the column vectors of \( A \) that forms a basis for the column space of \( A \).\[A = \begin{bmatrix} -2 & -4 & 4 & 5 \\ 3 & 6 & -6 & -4 \\ -2 & -4 & 4 & 9 \end{bmatrix}\]**Explanation for Educational Context:**In this example, matrix \( A \) is a \( 3 \times 4 \) matrix. The problem is asking to determine:a) The **rank** of \( A \), which is the dimension of the column space of \( A \) (the number of linearly independent columns), and the **nullity** of \( A \), which is the dimension of the null space of \( A \) (the number of linearly independent solutions to the homogeneous equation \( A\mathbf{x} = 0 \)).b) A subset of the columns of \( A \) that forms a basis for the column space of \( A \), indicating which columns are linearly independent and span the same space as all columns of \( A \).

The given matrix is: A=-2-44536-6-4-2-445 To find rank and nullity of matrix, first we…

Answered: Example 7: Find (a) the rank and…

Example 7: Find (a) the rank and nullity of A and (b) a subset of the column vectors of A that forms a basis for the column space of A. -2 -4 4 6. -6 -4 -2 -4 4 9.

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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