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Chapter 6: Q27E (page 309)

There exists a 4脳4 matrix whose entries are all 1or -1 , and such thatdetA=16.

Short Answer

Expert verified

Therefore, the given statement is false.

Step by step solution

01

Matrix Definition

A 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 determinant of similar matrices is equal.

So, det (A) must be equal to, det (2A)which is false.

If A is a 4脳4matrix with entries -1 or 1 , then all 24 of the addends in the definition of can be either - 1 or 1 .

If we want det A= 16, then twenty of them must be 1, and the remaining four be -1, which is impossible.

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Most popular questions from this chapter

For two invertible nxnmatrices A and B , what is the relationship between adj(A),adj(B),andadj(AB)?

Use Exercise 31 to find

det[1111112345149162518276412511681256625]

Do not use technology.

For an invertible nxn matrix A, what is the relationship between det (A) and det (A)?

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

8. [0000210003010040010500016]

Let Pn be the n脳n matrix whose entries are all ones, except for zeros directly below the main diagonal; for example,

role="math" localid="1659508976827" P5[1111101111101111101111101]

Find the determinant of Pn .
See all solutions

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