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 subspace 1 2 3 - 5 1 2 2 7 6 12 1 4 0 0 5 A = 2 0 0 0 4 - 1 12 4 8 11 0 0 0 A basis for Col A is given by (Use a comma to separate answers as needed.) The dimension of Col A is (Type an integer.) A basis for Nul A is given by { (Use a comma to separate answers as needed.) The dimension of Nul A is|. (Type an integer.) LO

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A: To Proof :-  If V  is a subspace of Rn , then there is a n × n  matrix A such that V = Col A.

Q: 11. A = 0-1 4 3 -9 9 -7 -2 3 10 -7 11 1 2 -3 2-5 5-8 7]

A: Introduction: To find the basis for column space and null space of a matrix you have to find the…

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A:

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Q: Please don't provide handwritten solution ...

A: Please comment down for any doubt. I hope my answer helps you.

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A: We can check whether the given statement is true or false.

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A: See detailed solution below. I have used thorem from linear transformation and some properties.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.