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Chapter 7: Q38E (page 338)

if A is a 2脳2matrix with t r A = 5and det A = - 14what are the eigenvalues of A?

Short Answer

Expert verified

The eigenvalues of A.

A=abcd,trA=5位2-5位-14=0(位+2)(位-7)=0位1=2,位2=7

Step by step solution

01

definition of matrix

A function is defined as a relationship between a set of inputs that each have one output.

A=abcd,trA=5

Now,

we solve: A = - 14

det(a-位濒)=0a-位bcd-位=0

02

definition of eigenvalues

The eigenvalue is a number that indicates how much variance exists in the data in that direction; in the example above, the eigenvalue is a number that indicates how spread out the data is on the line.

Multiply the matrix:

(a-位)(d-位)-bc=0位2-(a+d)位+ad-bc=0位2-5位-14=0(1-位)(2-位)=0

So,

位1=-2,位2=7

Hence,位1=-2,位2=7

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