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.

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.

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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Question

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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