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Asked Nov 12, 2019
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Linear algebra. please answer part (b)

(7) (a) Compute the determinant of A tI3, where A is given below. Here a1, a2, a3 are scalars.
0
0
ao
A
-1
0
-1
0
a2
(b) What is the determinant of A tIn, where A is given below and ao,. ., a-1 are scalars?
0
0
0
0
ao
-1
0
0
0
0
-1
0
0
A =
0
0 0
-1
an-1
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(7) (a) Compute the determinant of A tI3, where A is given below. Here a1, a2, a3 are scalars. 0 0 ao A -1 0 -1 0 a2 (b) What is the determinant of A tIn, where A is given below and ao,. ., a-1 are scalars? 0 0 0 0 ao -1 0 0 0 0 -1 0 0 A = 0 0 0 -1 an-1

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Expert Answer

Step 1

The determinant can be...

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0 0 -1 0 t 0 0 t A+,0 -1 0 t 0 0 -1 at 0 Using Rowoperations, divide first row by t and addto secondrow t 0 0 0 0 0 0 t t LA+,= -1 0 t а, 0 0 0 -1 a Use same operationup to last rowto obtain, t 0 0 0 0 0 t ,A+ 0 0 I 0 + t 0 0 0 0 a t t + Since this reduces to anuppertriangular matrix, the deteminantwould be the product of diagonal elements రో ఆ

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