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Chapter 6: Q49E (page 291)

Give an example of a3脳3 matrix with all nonzero entries such that detA=13.

Short Answer

Expert verified

Therefore, the example of 3脳3matrix is given by,

A=1111213213

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 m rows and n columns, the matrix is said to be a 鈥� m by n鈥� matrix, written 鈥� m脳n.鈥�

02

To find  3×3 matrix

We want to find amatrix,

A=abcdefghi , with all non-zero entries, such that:

aei+bfg+cdh鈭�ceg鈭�bdi鈭�afh=13

For a=b=c=1, we have

ei+fg+dh鈭�eg鈭�di鈭�fh=13

Forf=13,g=2,h=1 , we're left with:

.ei+d鈭�2e鈭�di=0

Ford=1,e=2,i=3, the equation applies.

So one example of such a matrix isA=1111213213

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Most popular questions from this chapter

29. IfA=u鈫�v鈫�w鈫�is a3脳3 matrix, then the formuladetA=V鈫�.u鈫�脳w鈫� must hold.

If all the diagonal entries of an n脳nmatrix Aare odd integers and all the other entries are even integers, thenA must be an invertible matrix.

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

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

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

There exists an invertible matrix of the form

[aefjb0g0c0h0d0i0]
See all solutions

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