If $$A=1223$$ and $$A2-$$λ$$A-I2=O$$ , then λ is equal to

$$A=1223$$ $$A2=12231223=58813$$ ⇒$$A2-$$λ$$A-I2=O$$ ⇒$$A2-I2=$$λA⇒λ$$A=48812=41223$$ ⇒λ$$=4$$

Operations of matrix

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If $A = [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}]$ and $A^{2} - λA - I_{2} = O,$ then $λ$ is equal to

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$A = [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}] A^{2} = [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}] [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}] = [\begin{matrix} 5 & 8 \\ 8 & 13 \end{matrix}] \Rightarrow A^{2} - λA - I_{2} = O \Rightarrow A^{2} - I_{2} = λA \Rightarrow λA = [\begin{matrix} 4 & 8 \\ 8 & 12 \end{matrix}] = 4 [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}] \Rightarrow λ = 4$

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Operations of matrix

Remember concepts with our Masterclasses.

If A=1223 and A2-λA-I2=O , then λ is equal to

A=1223 A2=12231223=58813 ⇒A2-λA-I2=O ⇒A2-I2=λA⇒λA=48812=41223 ⇒λ=4

Ready to Test Your Skills?

free study material

If $A = [\begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}]$ and $A^{2} - λA - I_{2} = O,$ then $λ$ is equal to