Transforming matrix t is given by
t=⎝⎛100240356⎠⎞
Characteristic polynomial of t is of form
λ3−D1λ2+D2λ−D3=0
Where D1= Sum of main diagonal element
=1+4+6=11
D2= Sum of minors of the main diagonal element
D2=∣∣4056∣∣+∣∣1036∣∣+∣∣1024∣∣
=24+6+4=34
D3=det∣t∣=1(24−0)+2(0−0)+3(0−0)
=24
Characteristic polynomial:
λ3−11λ2+34λ−24=(λ−1)(λ−4)(λ−6)
The minimum polynomial will have roots
1,4and6
Putting the matrix in the characteristic polynomial
T−1=⎝⎛000230355⎠⎞
T−4=⎝⎛−300200352⎠⎞
T−6=⎝⎛−5002−20350⎠⎞
⎝⎛000230355⎠⎞⎝⎛−300200352⎠⎞⎝⎛−5002−20350⎠⎞=⎝⎛000000000⎠⎞
∴ The minimal polynomial of t is
Mtx=(x−1)(x−4)(x−6)
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