A matrix A and an echelon form of A are shown below, Find a basis for Col A and a basis for Nul A. 4. 8 32 - 12 1 3 15 -7 A = 6 12 48 -18 0 1 7 -4 2 3 9 -2 0 0 0 Find a basis for Col A. (Simplify your answer. Use a comma to separate answers as needed.) Find a basis for Nul A. (Simplify your answer. Use a comma to separate answers as needed.)

A matrix A and an echelon form of A are shown below, Find a basis for Col A and a basis for Nul A. 4. 8 32 - 12 1 3 15 -7 A = 6 12 48 -18 0 1 7 -4 2 3 9 -2 0 0 0 Find a basis for Col A. (Simplify your answer. Use a comma to separate answers as needed.) Find a basis for Nul A. (Simplify your answer. Use a comma to separate answers as needed.)

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

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.

Question

A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A.
4
8 32 - 12
13 15 - 7
A =
6 12 48 - 18
0 1
7 -4
9.
- 2
0 0 0
Find a basis for Col A.
(Simplify your answer. Use a comma to separate answers as needed.)
Find a basis for Nul A.
(Simplify your answer. Use a comma to separate answers as needed.)

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Determine whether the statement below is true or false. Justify the answer. Here, A is an mxn matrix. The dimension of Col A is the number of pivot columns in A. Choose the correct answer below. O A. The statement is true. The pivot columns of A form a basis for Col A. Therefore, the number of pivot columns of A is the same as the dimension of Col A. O B. The statement is false. The number of pivot columns determines the dimension of the null space, not the column space. C. The statement is false. The dimension of Col A cannot be determined without the size of matrix A. O D. The statement is true. The number of pivot columns is equal to the number of free variables in the equation Ax = 0. The number of free variables in Ax = 0 is equal to the dimension of the column space.
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