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Chapter 6: Q20E (page 309)

There exists an invertible matrix of the form

[aefjb0g0c0h0d0i0]

Short Answer

Expert verified

Therefore, the given condition is not satisfied. So, the given statement is false..

Step by step solution

01

Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥渕 by n鈥� matrix, written 鈥� m脳n.鈥�

02

Given. 

Given matrix,

aefjb0g0c0h0d0i0

03

To check whether the given condition is true or false.

The fourth row of given matrix can always be obtained as a linear combination of the second and third row.

Therefore, the given condition is not satisfied. So, the given statement is false.

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