1. If A find (0) A+B, 0) A - B, () 24 - sc, (4) sa + 28 - 4C, ( AB, BA, (AB)C, (A) A(BC), (0 4" + B", ) FA".

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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| %oY l1. Ii.
H.W ch1.pdf →
Н.W
(2 -1B
=(), c = () find (e) A +B, () A - B,
1. If A=
(e) 24 - 3C, (4) 3A + 28 - 4C, (e AB, ) BA, () (AB)C, (k) A(BC). () A + B",
) B"A".
2 4
1 -1 2
1 -1
1 -2 3
B =
2
2. If A=
--2 1 3
2 -1 1
show that
-2
1
2
(A +B) =
A + AB + BA + B
3. prove that:
det (AB) = det (A) det (B)
If
4. (a) Find the inverse of the matrix A=
direet multiplication.
-2 2
1 2-3 and (b) check the answer by
41 2/
5. Solve the system of equations
(3z-2r + 2r, - 10
+ 2 - San,-1
4, + a+ 2rs =
(a) by Cramer's rule and (b) by using inverse matrices.
(3r, - 2+ 2-
2 + 2r, - 3a, = 0.
4, + + 2 =0
6. Solve
by Cramer's rule
7. For what values of k will the syatem
2z + ky + -0
(k- 1)z - v+ 2a = 0
4z+ y+4 e
have non-trivial solutions?
Selving formally by Cramer's rule
II
Transcribed Image Text:| %oY l1. Ii. H.W ch1.pdf → Н.W (2 -1B =(), c = () find (e) A +B, () A - B, 1. If A= (e) 24 - 3C, (4) 3A + 28 - 4C, (e AB, ) BA, () (AB)C, (k) A(BC). () A + B", ) B"A". 2 4 1 -1 2 1 -1 1 -2 3 B = 2 2. If A= --2 1 3 2 -1 1 show that -2 1 2 (A +B) = A + AB + BA + B 3. prove that: det (AB) = det (A) det (B) If 4. (a) Find the inverse of the matrix A= direet multiplication. -2 2 1 2-3 and (b) check the answer by 41 2/ 5. Solve the system of equations (3z-2r + 2r, - 10 + 2 - San,-1 4, + a+ 2rs = (a) by Cramer's rule and (b) by using inverse matrices. (3r, - 2+ 2- 2 + 2r, - 3a, = 0. 4, + + 2 =0 6. Solve by Cramer's rule 7. For what values of k will the syatem 2z + ky + -0 (k- 1)z - v+ 2a = 0 4z+ y+4 e have non-trivial solutions? Selving formally by Cramer's rule II
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