Can you please help solve this linear algebra review problem to review for my upcoming test, thank you. Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces.\[A = \begin{bmatrix}1 & 3 & 5 & -6 \\4 & 12 & 1 & 5 \\2 & 6 & -1 & 10 \\6 & 18 & 0 & 16 \\\end{bmatrix}\sim\begin{bmatrix}1 & 3 & 5 & 2 \\0 & 0 & 2 & -5 \\0 & 0 & 0 & 2 \\0 & 0 & 0 & 0 \\\end{bmatrix}\]A basis for Col A is given by: [ ](Use a comma to separate answers as needed.)

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Answered: Given below is a matrix A and an…

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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Can you please help solve this linear algebra review problem to review for my upcoming test, thank you.

Given below is a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces.

\[
A = \begin{bmatrix}
1 & 3 & 5 & -6 \\
4 & 12 & 1 & 5 \\
2 & 6 & -1 & 10 \\
6 & 18 & 0 & 16 \\
\end{bmatrix}
\sim
\begin{bmatrix}
1 & 3 & 5 & 2 \\
0 & 0 & 2 & -5 \\
0 & 0 & 0 & 2 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]

A basis for Col A is given by: [ ]

(Use a comma to separate answers as needed.)

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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