TYPE-1
A) Construct a 2x 3 matrix A= [aᵢⱼ] whose elements aᵢⱼ are given by:
a) aᵢⱼ= i x j 1 2 3
2 4 6
b) aᵢⱼ= 2i - j 1 0 -1
3 2 1
c) aᵢⱼ= i+ j 2 3 4
3 4 5
d) aᵢⱼ= (i+ j)²/2. 2 9/2 8
9/2 8 25/2
B) Construct a 2 x 2 matrix A= [aᵢⱼ] whose elements are given by:
a) aᵢⱼ = (i+ j)²/2 . 2 9/2
9/2 8
b) aᵢⱼ= (i - j)⅖/2. 0 1/2
1/2 0
c) aᵢⱼ= (i - 2j)²/2. 1/2 9/2
0 2
d) aᵢⱼ = |2j -3j|/2. 1/2 2
1/2 1
C) Construct a 3 x 4 matrix A= [aᵢⱼ] whose elements aᵢⱼ are given by:
a) aᵢⱼ= i + j. 2 3 4 5
3 4 5 6
4 5 6 7
b) aᵢⱼ= 2i. 2 2 2 2
4 4 4 4
6 6 6 6
c) aᵢⱼ= (1/2) |-3i + j| 1 1/2 0 1/2
5/2 2 3/2 1
4 7/2 3 5/2
D)1) If A= [aᵢⱼ] is a matrix given by
A= [aᵢⱼ]= 4 -2 1 3
5 7 9 6
21 15 18 -25
Write
a) the order of A. 3x 4
b) the elements a₂₄. 6
b) the element a₃₄. -25
c) verify a₃₂ = a₂₃ + a₂₄.
2) If A= [aᵢⱼ]= 2 3 -5 and B= 2 -1
1 4 9 -3 4
1 2 then find
a) a₂₂ + b₂₁. 1
b) a₁₁b₁₁ + a₂₂b₂₂. 20
Type - 2
1) If 3x+4y 2 x- 2y = 2 2 4
a+ b 2a - b -1 5 -5 -1 then find x, y, a, b. 2, -1, 0, 5
2) If x 3x - y = 3 2
2x+z 3y- a 4 7 then find x, y, z ,a. 3,7,-2,14
3) if x- y z = -1 4
2x - y a 0 5 then find x, y, z, a. 1,2,4,5
4) If x+ 3 z+ 4 2y -7 0 6 3y-2
4x+6 a-1 0 = 2x -3 2c+2
b -3 3b z+ c 2b+4 -21 0 find a, b, c, x, y and z. -2, -7, -1, -3, -5, 2
5) If xy 4 = 8 a
z+ 6 x+y 0 6 then find the value of x, y, z, a. 2.4, -6,4 or 4,2,-6,4
6) If A= 2x +1 2y & B= x +3 y²+2
0 y²- 5y 0 -6 and A = B then find the value of x and y.
7) if x+ 10 y²+ 2y = 3x +4 3
0 -4 0 y²- 5y then find the value of x, y. 3,1
8) If A= a+ 4 3b & B= 2a +2 b²+2
8 -6 8 b²-10 with the relation A= B, then find x, y. 2,2
EXERCISE - B
Type - 1
1) If A= 3 -2 & B= -2 4
1 4 1 3
Find A+ B. 1 2
2 7
2) 2 1 3 1 -2 3
If A= 0 3 5 2 6 1
-1 2 5 0 -3 1
Find A+ B. 3 -1 6
2. 9 6
-1 -1 6
3) Let A= 2 4 B= 1 3 & C= -2 5
3 2 -2 5 3 4 then find
a) 2A - 3B. 1 -1
12 -11
b) B - 2C. 9 -17
-14 -11
c) 3A - C. 8 7
6 2
d) 3A - 2B + 3C. -2 21
22 8
4) If A= 2 3 B= -1 0 2 & C= -1 2 3
5 7 3 4 1 2 1 0 find
a) A+ B.
b) B + C. -2 2 5
5 5 1
c) 2B + 3A.
d) 3C - 4B. 1 6 1
-6 -13 -4
5) Let A= -1 0 2 & B= 0 -2 5 & C= 1 -5 2
3 1 4 1 -3 1 6 0 -4
Find 2A - 3B + 4C. 2. -14 -3
27 11 -11
6)
ᵢⱼᵢⱼᵢⱼᵢⱼᵢⱼ