H. W -1
SAP- 1
1) If A= 2 0 3 & B= 1 2 3
1 2 0 2 1 4 find A+ B
2) If A= 1 2 3 & B= 1 2
4 5 6 3 4
6 8 9 5 6 find A+ B
3) If A= 0 2 3 & B= 7 8 3
2 1 4 1 4 3 find
a) 2A + 3B
b) 3A - B
c) AB
4) If A= 1 3
3 4 and A²- kA - 5=0, then find k.
5) If A= x y z & B= a h g & C= x
h b f y
g f c z
Then show ABC= ax²+ by²+ cz²+ 2fyz + 2gzx+ 2hxy.
6) If A= 1 0 & B= 0 1
0 1 -1 0
Then show that (aA+ bB)(cA+ dB)= (ac - bd)A+ (ad + bc)B.
7) If A= 1 0 0 & B= x₁ y₁ z₁
0 1 0 x₂ y₂ z₂
0 0 1 x₃ y₃ z₃
Then show that AB= BA = B
Sap-2 (H. W)
1) If A= 1 -1 & B= a 1
2 -1 b -1 and (A+ B)¹= A²+ B², find a, b, using the value of a, b, verify whether AB= BA.
2) If A= 1 -1
1 1 show A/√2 is a orthogonal matrix. A. A'= I is orthogonal matrix
3) Find the inverse of A
A= 1 -3 2
2 5 -1
-3 1 4
4) A= 20 10
10 20 find inverse of A
5) Solve: x + 2y - z= 9, 2x - y - 4z= -7; 3x + 2y - 3z= 2.
SAP-1
1) If A= 2 -1
-1 2 and I is the unit matrix of order 2, then A² is equal to
a) 4A - 3I b) 3A - 4I c) A - I d) A + I
2) The multiplicative inverse of
2 1
7 4 is
a) 4 -1 b) 4 -1 c) 4 -7 d) -4 -1
-7 -2 -7 2 7 2 7 -2
3) Assuming that the sums and products given below are defined, which of the following is not true for matrices?
a) AB= AC does not imply B= C
b) A+ B= B+ A
c) (AB)'= B'A'
d) AB= O implies A= O or B= O.
4) If A=1. 0 2 & Adj A= 5 a -2
-1 1 -2 1 1 0
0 2 1 -2 -2 b
Then the values of a and b are
a) a= -4, b= 1 b) a= -4, b= -1 c) a= 4, b= 1 d) a= 4, b= -1
5) If A= -1 0
0 2 then the value of A³- A² is
a) I b) A c) 2A d) 2I.
6) If A= -x - y
z t, then transpose of adj A
a.) t z b) t y c) t -z d) none
-y -x -z -x y -x.
7) If A square metrix of order 3x3 and λ is a scalar, then adj(λA) is equal to
a) λ adj A B) λ² adj A c) λ³ adj A d) λ⁴ adj A.
8) The inverse of 5 -2
3 1
a) -2/13 5/13 b) 1 2 c) 1/11 2/11 d) 1 3
1/13 3/13 -3 5 -3/11 5/11 -2 5
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