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Chapter 6: Q42E (page 309)

If all the diagonal entries of an n脳nmatrixA are even integers and all the other entries are odd integers, then Amust be an invertible matrix.

Short Answer

Expert verified

Therefore, detA=0and the Ais non-invertible. So, the given statement is false.

Step by step solution

01

Matrix Definition

Matrix is aset 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�m by n鈥� matrix, written 鈥�m脳n.鈥�

02

To check whether the given condition is true or false

For example,

A=01110-1110

This matrix has even diagonal entries and odd entries outside the diagonal, howeverdetA=0.

So, A is non-invertible. So, the given statement is false.

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Most popular questions from this chapter

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

4.[1-12-2-1216211410-261033]

Question:We say that a linear transformation Tfrom N3toN3to preserves orientation if it transforms any positively oriented basis into another positively oriented basis. See Exercise 19. Explain why a linear transformationT(x鈫�)=Ax鈫�preserves orientation if (and only if) detAis positive.

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

8. [0000210003010040010500016]

Use Exercise 31 to find

det[1111112345149162518276412511681256625]

Do not use technology.

Use Cramer's rule to solve the systems in Exercises 22 through 24.

23. |5x1-3x2=1-6x1+7x2=0|
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