Question

The product of the Eigen values of
1 0 01
A=0 3 -1 is equal to
10 -1 3.​

Answer 1

Answer:

no idea but 10-1 3 i hope is correct ans

Answer 2

The correct question: Find out the eigen values of following matrices: $\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]$, and $\left[\begin{array}{ccc}1&0\\3&-1\\\end{array}\right]$.

The correct answer is given below.

Given:

The 2 determinants are given : $\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]$, $\left[\begin{array}{ccc}1&0\\3&-1\\\end{array}\right]$.

To Find:

We have to find the eigen values of given matrices using the following formula.

|A-λI| = 0

A is the square matrix, λ is the eigen matrix and I is the identity matrix.

Solution:

First we can find the eigen value of first matrix.

$\left[\begin{array}{ccc}1-λ&0\\0&1-λ\\\end{array}\right] = 0$

$(1-λ)^{2}-0 = 0$

$λ^{2} - 2λ + 1 = 0$

Using the formula $-b$±$\frac{\sqrt{b^{2}-4ac } }{2a}$, above equation becomes,

$2±\frac{\sqrt{2^{2}-4 } }{2} = \frac{2}{2} = 1.$

Similarly, the eigen value of second matrix can be found out as follows.

$\left[\begin{array}{ccc}1-λ&0\\3-λ&-1\\\end{array}\right] = 0$

Simplifying above formula we get,

$λ^{2} - 1 = 0\\\\λ = ±1.$

Eigen values of first matrix = 1.

Eigen values of second matrix = ±1.

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