Question

the matrix [4 2 2 4] ,find the corresponding to the Eigen vectors [101 101].​

Answer 1

Let P={-1,1} , Q={| 2 = 4, ∈ } and R = {-2,-1,1} . State which of the following are TRUE and which are FALSE. (i)P↔Q (ii)P=Q (iii)Q↔R (iv)P↔R (v)Q=R (vi)P=R

Answer 2

The eigenvalues are 6 and 6.

Given:

A matrix =  $\left[\begin{array}{cc}4&2\\2&4\end{array}\right]$

An eigenvector =  $\left[\begin{array}{c}101\\101\end{array}\right]$

To Find:

The eigenvalues with respect to the given eigenvector.

Solution:

We can simply solve this problem by using the following mathematical process.

Let the given matrix be 'A' and the eigenvector be 'X'.

Let k be the eigenvalue

We know,

AX = kX

Therefore,

$\left[\begin{array}{cc}4&2\\2&4\end{array}\right]\left[\begin{array}{c}101\\101\end{array}\right]=\left[\begin{array}{cc}k_{1} &0\\0&k_{2} \end{array}\right] \left[\begin{array}{c}101\\101\end{array}\right]$

$\left[\begin{array}{c}606\\606\end{array}\right]=\left[\begin{array}{c}101k_{1} \\101k_{2} \end{array}\right]$

$101k_{1} =606$ and $101k_{2} =606$

So,

$k_{1} =6$ and $k_{2} =6$

Hence, the eigenvalues are 6 and 6.

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