deta i2 4 11 54 2 7 10 c as 2 12

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Unformatted text preview: − λ) + 54 = λ2 − 7λ + 10. (c.) As λ2 − λ − 12 = (λ − 2)(λ − 5), the roots are λ1 = 2 and λ2 = 5. 1 0 −3 1 1 5 2 0 2 −5 0 −→ 1 0 −7 16 0 20 −45 1 −1 2 1 Then L = [E32 ( 1 )E31 ( 4 )E21 ( 1 )]−1 = E21 (− 1 )E31 (− 1 )E32 (− 1 ) = − 1 3 4 4 4 3 4 1 8 3 1=U 0 0 1 0 1 −3 0 0 1 13 3 1 115 −→ 0 −5 00 −5 0 −8 2 −23 −5 (3.) Row reduce: 12 0 8 12 08 12 1 E21 ( 1 ) E31 ( 4 ) 4 −3 3 −1 −→ 3 1 −→ 0 0 −3 −1 2 −3 −1 2 0 −4 −9 λ − (4a.) A − λI2 = 6 11 0 1 −40 115 −→ −5 −4 −9 2 − (di.) A − λ1 I2 = A − 2I2 = 6 11 0 −4 −9 5 − (dii.) A − λ2 I2 = A − 5I2 = 6 11 0 −6 −9 = 2 6 9 0 0 −9 −9 = 5 6 6 −6 −9 −9 −9 0 = (diii.) (A − λ1 I2 )(A − λ2 I2 ) = (A − 2I2 )(A − 5I2 ) 6 9 6 6 0 2 0 0...
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