Exercise - A
1)a) A= 8 -3 & B= 4 -5
Find
a) A+ B
b) A- B
c)!B - A
2) If A= 2 B= 1 & C= 6
5 4 -2 find
a) A+ B
b) B+ C
c) A- C
d) C - B
e) A+ B - C
f) A- B + C
3) If A= 2 5 and B= 1 -3
-3 7 2 5
Find A+ B. 3 2
-1 12
4) If A= 2 -3 and B= -1 6
4 5 3 2
Find 2A+ 5B. -1 24
23 20
5) If M= 2 0 and N= 2 0
1 2 -1 2
Find M+ 2N. 6 0
-1 6
6) If A= 2 0 and B= 1 2
-3 1 3 1
Find 3A+ 4B. 10 8
3 7
7) If A= 1 4 and B= -4 -1
2 3 -3 -2
Find 2A+ B. -2 7
1 4
8) If A= 2 4 and B= 1 3
3 2 -2 5
Find 2A+ 3B. 7 17
0 19
9) If A = -3 5 and B= 2 -3
-9 11 6 7
find 2A + 3B. 0 1
0 1
Exercise - B
1) If A= 3 -1 7 & B= 2 -2 -1
0 1 2 1 2 3
Find A+ B. 5 -3 6
1 3 5
2) If A= 0 2 3 & B= 7 6 3
2 1 4 1 4 5
Find 2A+ 3B. 21 22 15
7 14 23
3)
* SUBSTRACTION OF MATRICES *
Exercise - C
1) If A = 2 4 and B = 3 6
5 6 5 4
Find A- B. -1 -2
0 2
2) 1 2 & B= 5 6
3 4 7 8 Find
A) B - A. 4 4
4 4
B) 1/4(B - A). 1 1
1 1
2) If M= 2 0 and N= 2 0
1 2 -1 2
Find:
A) 2M - 3N. -2 0
5 -2
B) 2(M - 3N). 16 0
8 -8
C) 2M - N. 2 0
3 2
3) If A= 7 6 3 and B = 0 2 3
1 4 5 2 1 4
Find 3B - A. 21 16 6
1 11 11
4)
Exercise - D
1) If A= 2 1 B= 1 0 & C= 0 2
0 1 2 4 1 4 Find 2A+ 4B - 3C. 8 -4
5 6
2) if A= 1 2 B= -2 3 C= 0 3
-2 3 1 2 2 -1
find
i) A + 2B - 3C. -3 -1
-6 10
ii) 3A - 4B + C. 11 0
-6 -1
iii) A - 3B + 2C. 7 -1
-1 -5
3) If A= 2 4 B= 3 5 & C= 1 -1
0 3 1 4 2 1 find 3A - 2B + 2C. 2 0
2 3
4) If A = 2 4 and B = 3 6
5 6 5 4
find X if 3A + 4B - 2X= 0. 9 18
35/2 22
5) If A = 4 2 and B = 3 5
-3 5 1 2
find X if A -B +X= 0. -1 3
4 -3
6) If A= 5 4 & B= 2 1 C= -3 2
3 -1 0 4 1 0
Find
a) A+ C. 2 6
4 -1
b) B- A. -3 -3
-3. 5
c) A+ B - C
7) If A= 8 6 & B= -3 5
-2 4 1 0 then solve 2x2 matrix X:
a) A+ X - B -11 -1
3 -4
b) X - B = A. 5 11
-1 4
** EQUALITY OF TWO MATRICES:
Exercise- E
1) x 7 + 6 -7 = 20 7
9 y-5 4 5 22 15
find x and y. 14, 22
2) a 3 + 2 1 - 1 b = 5 0
4 2 1 -2 -2 c 7 3
find a, b, c. 4, -1,3
3) If A=2 a B = -2 3 C = c 9
-3 5 7 b -1 -11
and 5A + 2B = C find a, b, c. 6/5, -18,6
4) If X + Y = 7 0 and X - Y= 4 -1
2 3 5 -2
find metrices X And Y.
11/2 -1/2 3/2 1/2
7/2 1/2 -3/2 5/2
5) If A+B= 2 2 and A - B= 5 4
0 2 0 5
Find the metrices A and B.
7/2 3 -3/2 -1
0 7 0 -3/2
7) If A= x y+2 & B= 3 1
3 z -1 3 2 with the relation
A= B, then find x,y,z. 3,-1,3
8) If A= -4 a+5 & B= b+4 2
3 2 3 c-1 with the relation A= B then find a,b,c. -3,-8,3
9) If A= a a-b & B= 3 -1
b+c 0 2 0 with the relation A= B, find a,b,c. 3,4,-2
10) If A= a+2 b-3 & B= 2a-3 4b+1
-1 3+c -1 5c-7 with the relation A= B, find a,b,c. 5,-4/3,2.5
11) If A= x B= 3 & C= 6
-2 y -4 with the relation A+ B = C then find x, y. 3,-2
12) If A= 5 2 B= 1 x-1 & C= 4 7
-1 y-1 2 -3 -3 2 with the relation A- B = C, find x,y. -4,0
13)
EXERCISE - F
1) If A = 1 3 B = 4 -5
2 -2 3 -1 Find
i) AB. 13 -8
2 -12
ii) BA. -6 22
1 11
iii) A². 7 -3
-2 10
iv) (AB)². 155 8
2 128
v) A² - B². 6 -8
-11 24
vi) A² - 2B. -1 7
-8 12
2) If A= 1 2 & B= 5 6
3 4 7 8 Find
A) AB. 19 22
43 50
B) BA. 23 34
31 46
3) If A = 1 2 B= 3 4 C= -1 0
5 -4 0 2 2 -2
find i) ABC
ii) (A+B)C
iii) A² - BC
iv) AC + B²
v) (A+ B) (A - B)
vi) AC + B²
4) If A= 1 -1 and B= 1 1
-1 1 1 1
prove AB=0.
5) Let A= 4 -2 B= 0 2 & C= -2 0
6 -3 1 -1 1 -3
Find
A) A². 4 -2
6 -3
B) BC. 2 -6
-3 3
C) A²- A + BC. 2 -6
-3 3
) If A= 1 0 B= 2 0 & C= -1 2
1 1 1 1 3 1 Show that
A) A(B+ C)= AB + AC
B) (B+ C)A = BA + CA ≠ A(B + C)
5) If A= 1 & B= 1 2 find BA
2
6) If A= 3 -2 & B= 2 find BA
0
7) If A= -1 0 B= a b & C= 1 0
0 1 c d 0 -1 find a, b, c, d when AB = C. -1,0,0,-1
8) If A= 1 0
0 -1 show that
A) A²≠ A.
B) A³= A.
15) If A = 2 -1 show A² - 4A + 3I =0
-1 2
16) If A= 1 -1 & B= 1 2
1 -1 4 -1 show that (A+ B)²≠ A²+ B².
) if A= -3 2 & B= 1 a
-2 -4 b 0 and (A+ B)(A- B)= A²- B²
17) If A = a b
c d
show A² - (a+d)+(ad-bc) =0
18)
19) A= 1 -1 and B = 1 x
2 -1 4 y and
(A +B)² = A² + B² then find x,y.
) A= 11 & B= 1 2
12
And the relation MA = B
A) State the order of the Matrix. 1x2
B) Find the Matrix N. 0 1
) If A= 3 -4 B= x & C= 17
4 5 y 2 and AB= C then find the value of x, y. 3,-2
) If A= 3 -3 B= x & C= 4
5 -4 y 8 and the relation AB= C , show x= 2y.
) If A= 2 2
m n find m and n so that A²= 0. -2,-2
) If A= 1/4 3/4
h k fund h and k so that A² = I. 5/4,-1/4
) Let A= 1 4 & B= 2 m
0 -1 0 -1/2 Find the value of m if AB = BA. 5
) If A= a b B= a 6 & C= 4 a+ b
c d -1 2d c+ d 3 and the relation 3A = B+ C. Then find the value of a, b, c are d. 2,4,1,-3
) If A= 2 -1 B= -3 5
2 0 4 3 and the relation A+ 2N= B, then the Matrix N. -5/2 3
1 3/2
Exercise - G
1) construct a 2 x 2 matrix A = [aᵢⱼ] whose elements are given by
aᵢⱼ = (i+ 2j)²/2
Exercise - H
49) if A= 2 -1
-1 2
Prive A² - 4A + 3I =0.
50) If A = 1 1 prove A² - 4A +5I=0
2 3
51) If A = 4 5
5 6 Prove A² - I=10A
56) If A= 3 2
2 1
Prove A² - 4A - I= 0 where I= 2x2 metrics and 0 is Null metrics.
58) If A= 2 -1
-1 2
Prove A² - 4A + 3I = 0 where I= 2x2 metrics and 0 is Null metrics.
EXERCISE - I
1) If A= 2 1 3 & B= 3 -2
4 -3 2 7 4
Find transpose matrix Aᵗ and Bᵗ
If possible, find
a) A+ Aᵗ
b) B+ Bᵗ
2) Write the transpose of the following:
a) 3 -1
b) 5 -6
2 1
c) -4
0
d) 2 0 -1
3 3 -2
Also state the order of transpose matrix obtained.
3) Given A= (3 1); find its transpose matrix Aᵗ. If possible, find A+ Aᵗ.
4) If M= 5 -3
-2 4 find its transpose matrix Mᵗ. If possr, find
a) M+ Mᵗ
b) Mᵗ - M
MISCELLANEOUS -1
1) Write the additive inverse of matrix A, B and C, where
A= (6 -5
B= -2 0
4 -1
C= -7
4
2) Given A=(2 -3), B=(0 2) and C=(-1 4); find the matrix X in each case of the following:
a) X = A+ B - C
b) X + B = C - A
c) A - X = B + C
d) A - C = B - X
3) Given A= -1 0 B= 3 -3
2 -4 -2 0 find the matrix X in each case of the following:
a) A+ X = B
b) A - X = B
c) X - B = A
Continue.......
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