Question

if 1 2 3 are eigenvalues of a then eigenvalues of A-3I

Answer 1

Answer:

The eigen values of $A-3I$ are $-2,-1,0$

Step-by-step explanation:

Tip:

• The every Square matrix satisfies its characteristic root or  Eigen values. This statement is given by the Cayley Hamilton Theorem

Step 1 of 1:

• Given: Eigen values of Matrix A are 1,2,3
• By putting the value of eigen values in the place of A gives the value of the Eigen Value of $A-3I$
• The Eigen Values of $A-3I$are

• $A-3I$

      $=1-3\\=-2$

• $A-3I$

        $=2-3\\=-1$

• $A-3I$

      $=3-3\\=0$

Answer 2

If 1 , 2 , 3 are eigen values of A then eigen values of A - 3I are - 2 , - 1 , 0

Given :

1 , 2 , 3 are eigen values of A

To find :

The eigen values of A - 3I

Concept :

c is a eigen value of A if and only if c - 3 is a eigen value of A - 3I

Solution :

Step 1 of 2 :

Write down eigen values of A

Here it is given that 1 , 2 , 3 are eigen values of A

Step 2 of 2 :

Find eigen values of A - 3I

We know c is a eigen value of A if and only if c - 3 is a eigen value of A - 3I

First eigen value of A = 1

∴ First eigen value of A - 3I = 1 - 3 = - 2

Second eigen value of A = 2

∴ Second eigen value of A - 3I = 2 - 3 = - 1

Third eigen value of A = 3

∴ Third eigen value of A - 3I = 3 - 3 = 0

Hence eigen values of A - 3I are - 2 , - 1 , 0

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