(Linear algebra)Pls answer question asapWrite work neatly and box final answersThanks Consider the matrix \( A = \begin{bmatrix} 1 & 3 & -4 & 2 \\ 0 & 1 & -1 & 3 \\ -2 & -6 & 8 & -4 \end{bmatrix} \).For each of the following, be sure to show work!1. Find a basis for the null space of \( A \).2. Find a basis for the column space of \( A \).3. Find the rank of the matrix \( A \).4. Find the nullity of matrix \( A \).

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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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(Linear algebra)

Pls answer question asap

Write work neatly and box final answers

Thanks

Consider the matrix \( A = \begin{bmatrix} 1 & 3 & -4 & 2 \\ 0 & 1 & -1 & 3 \\ -2 & -6 & 8 & -4 \end{bmatrix} \).

For each of the following, be sure to show work!

1. Find a basis for the null space of \( A \).
2. Find a basis for the column space of \( A \).
3. Find the rank of the matrix \( A \).
4. Find the nullity of matrix \( A \).

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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