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Chapter 6: Q45E (page 308)

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

Short Answer

Expert verified

Therefore, the adj(A)=ATis given by,

A=ab-ba.

Step by step solution

01

Matrix Definition. 

Matrix is a set of numbersarranged in rows and columns soas 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�m byn鈥� matrix, written 鈥�.鈥�

02

To find adj(A)=AT.

Let,

A=abcd

Then, we have

AT=acbd,

and

adjA=d-b-ca

For AT=adjA, we need a=dand b=-c.

Thus,

A=ab-ba.

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Most popular questions from this chapter

If Ais an invertible n脳n matrix, thendet(AT) must equaldet(A-1).

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

If all the entries of a square matrixAare integers and detA=1 , then the entries of matrix A-1 must be integers as well.

What are the lengths of the semi axes of the largest ellipse you can inscribe into a triangle with sides 3,4 , and 5 ? See Exercise 48.

If all the entries of a 7脳7matrix A are 7, then detA must be 77.
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