5. (a) Let 10-1 1 -1 -1 -1 1 P = 0 1 1 -1 2 -2 2 2 Evaluate the determinant of P. [4] (b) Suppose that A and B are n x n, invertible matrices, n ≥ 2. Let |A| = a and |B|= b. Find the values of the following determinants in terms of a, b and n: (i) |45|; (ii) |BT |; (iii) | AB-2|; (iv) |3BA|.
5. (a) Let 10-1 1 -1 -1 -1 1 P = 0 1 1 -1 2 -2 2 2 Evaluate the determinant of P. [4] (b) Suppose that A and B are n x n, invertible matrices, n ≥ 2. Let |A| = a and |B|= b. Find the values of the following determinants in terms of a, b and n: (i) |45|; (ii) |BT |; (iii) | AB-2|; (iv) |3BA|.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![5. (a) Let
10-1
1
-1 -1 -1
1
P
=
0 1 1
-1
2
-2
2
2
Evaluate the determinant of P.
[4]
(b) Suppose that A and B are n x n, invertible matrices, n ≥ 2. Let |A| = a
and |B|= b. Find the values of the following determinants in terms of
a, b and n:
(i) |45|;
(ii) |BT |;
(iii) | AB-2|;
(iv) |3BA|.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56349570-c850-4378-b43a-2d1a85030776%2F50fe4a0a-9ddb-4e0b-9468-524032ba06d4%2F2zsd1x_processed.png&w=3840&q=75)
Transcribed Image Text:5. (a) Let
10-1
1
-1 -1 -1
1
P
=
0 1 1
-1
2
-2
2
2
Evaluate the determinant of P.
[4]
(b) Suppose that A and B are n x n, invertible matrices, n ≥ 2. Let |A| = a
and |B|= b. Find the values of the following determinants in terms of
a, b and n:
(i) |45|;
(ii) |BT |;
(iii) | AB-2|;
(iv) |3BA|.
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