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Chapter 6: Q41E (page 309)

If all the diagonal entries of an n脳nmatrix Aare odd integers and all the other entries are even integers, thenA must be an invertible matrix.

Short Answer

Expert verified

Therefore, A is invertible. So, the given statement is true.

Step by step solution

01

Matrix Definition

Matrix is aset of numbers arranged in rows and columns so as to form a rectangular array.

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

Using the definition ofdetA, the product in the addend corresponding to the diagonal pattern is odd, while all other addends are even.

Thus,detAis odd, so it must be different than 0.

Thus, A is invertible. So, the given statement is true.

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Most popular questions from this chapter

Matrix[910037541008100987654100]is invertible.

29. IfA=u鈫�v鈫�w鈫�is a3脳3 matrix, then the formuladetA=V鈫�.u鈫�脳w鈫� must hold.

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

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

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

9. [1111112222113331114411115]

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

7. [0000100012001230123412345]
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