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Chapter 6: Q28E (page 309)

If the determinant of a2脳2 matrix is 4, then the inequality |Av鈫�|鈮�4|v鈫�| must hold for all vectors v鈫� in.

Short Answer

Expert verified

Therefore, the given statement is true.

Step by step solution

01

 Step 1: 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 鈥渕 by n 鈥� matrix, written 鈥� m脳n.鈥�

02

To check whether the given condition is true or false

Let,

A=4401.

Clearly,

det A = 4 , however, for

V=11

We have,

Av=81Av=65>32Av=4v

Therefore, the given statement is true.

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Most popular questions from this chapter

Consider the function F(A)=F[v鈫�w鈫�]=v鈫�脳w鈫�from 鈩�2脳2 to鈩�, the dot product of the column vectors of A.
a. Is Flinear in both columns of A? See Example 6.
b. Is F linear in both rows of A?
c. Is Falternating on the columns of A? See Example 4.

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

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

6.[111111441-12-21-18-8]

There exists a real 3脳3matrix Asuch thatA2=-l3.

If A and Bare invertible n脳nmatrices, and if Ais similar toB, isadj(A) necessarily similar to adj(B)?
See all solutions

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