Suppose A is a 5×7 matrix. How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. O B. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R. O C. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.

Suppose A is a 5×7 matrix. How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. O B. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R. O C. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R5? Why?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The matrix must have
pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution.
O B. The matrix must have
pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R.
O C. The matrix must have
pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent.
O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.

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