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Chapter 6: Q12E (page 309)

det[0100001000011000]=1

Short Answer

Expert verified

Therefore, the given condition is not satisfied. So, it is false statement.

Step by step solution

01

Definition. 

A determinant is a unique number associated with a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

02

To check whether the given condition is true or false.

Given,

det[0100001000011000]=1

We compute,

det[0100001000011000]=-13det[1000010000100001]=-1

Therefore, the given condition is not satisfied. So, it is false statement.

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Most popular questions from this chapter

Find the 3-volume of the 3-parallelepiped defined by the vectors

[1000],[1111],[1234].

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

positive or negative? How can you tell? Do not use technology.

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

a. Find a noninvertible 2脳2matrix whose entries are four distinct prime numbers, or explain why no such matrix exists.

b. Find a noninvertible 3脳3matrix whose entries are nine distinct prime numbers, or explain why no such matrix exists.

If twon脳n matrices A and B are similar, then the equationdetA=detB must hold.
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