Question

8 8 -2
4 -3 -2
3 -4 1 diagonalize the matrix

Answer 1

Answer:

The characteristic eq. of A is

∣∣∣∣8−λ43−8−3−λ−4−2−21−λ∣∣∣∣=0

Simplifying we get

∴(8−λ)[(−3−λ)(1−λ)−8]+[4(1−λ)+6]−2[−16+9+3λ]=0∴(8−λ)[−3−λ+3λ+λ2−8]+8[4−4λ+6]−2[−7+3λ]=0∴(8−λ)[λ2+2λ−11]+80−32λ−6λ+14=0∴−λ3−2λ3+11λ+8λ2+16λ−88+904−38λ=0∴−λ3+6λ2−11λ+6=0∴λ=3,2,1

For λ=1[A−λI]X=0⎡⎣⎢743−8−4−4−2−20⎤⎦⎥⎡⎣⎢x1x2x3⎤⎦⎥=⎡⎣⎢000⎤⎦⎥7x1−8x2−2x3=04x1−4x2−2x3=0

By cramer's rule

x1∣∣∣−8−4−2−2∣∣∣=−x2∣∣∣74−2−2∣∣∣=x3∣∣∣74−84∣∣∣∴x18=x26=x34∴x14=x23=x32

Step-by-step explanation:

Hope this helps you

thank you

Answer 2

Answer:

Step-by-step explanation: