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Chapter 6: Q10E (page 308)

An8脳8matrix fails to be invertible if (and only if) its determinant is nonzero.

Short Answer

Expert verified

Therefore, 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 rectangular array.

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

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

02

To check whether the given condition is true or false.

We know that,

An8脳8 matrix is invertible if and only if its determinant is non-zero.

So, the statement is false

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Most popular questions from this chapter

In Exercises 62 through 64, consider a function D from 鈩�2脳2 to鈩� that is linear in both columns and alternating on the columns. See Examples 4 and 6 and the subsequent discussions. Assume thatD(l2)=1.


62. Show thatD(A)=0for any2脳2matrix whose two columns are equal.

25. If the determinant of a square matrix is -1, then Amust be an orthogonal matrix.

Show that A(adjA)=0=(adjA)Afor all noninvertible n脳nmatrices A. See Exercise 42.

There exists a nonzero4脳4 matrixAsuch thatdetA=detA(4A).

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

3.[13241648130026412]
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