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Chapter 6: Q54E (page 276)

Is the determinant of the matrix

A=[1100023456710008100098765432100012100034]

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

Short Answer

Expert verified

Therefore, the given matrix of determinant is positive.

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

Given. 

Given Matrix,

A=[1100023456710008100098765432100012100034]

03

To find the given matrix is positive or negative.

The pattern containing all the 1000 's corresponds to the permutation.

p=1234524153, which is an even one. Thus, its addend to the determinant computation is positive. Other addends are, by modulus, too small to change the determinant's sign even if they're negative. Therefore, this matrix's determinant is positive.

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Most popular questions from this chapter

det(A+B)=detA+detBfor all5脳5 matricesA andB.

A square matrix is called a permutation matrix if each row and each column contains exactly one entry 1, with all other entries being 0 . Examples are In,[010001100], and the matrices considered in Exercises 53 and 56 . What are the possible values of the determinant of a permutation matrix?

det[0100001000011000]=1

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

Find all 2脳2 matrices Asuch thatadj(A)=AT.
See all solutions

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