Page 341 - Artificial Intellegence_v2.0_Class_11
P. 341
Practical Questions
1. Find the Transpose of the following matrix.
2 –5 3
Ans. 2 –1 –1 0 2/5
–5 0
3 2/5
2. If A = B, then find the value of x, y and z.
x + 2 2 6 2
A = B =
z – 5 xy 10 8
Ans. As A=B, so x+2 = 6
x = 6 – 2 = 4
xy = 8
(Putting x=4), 4y=8 y = 8/4 =2
z – 5 = 10 z = 10+5 = 15
Hence, x=4, y=2 and z=15
1 3
–1
3. Find A + A if A = 2 4
1 3
Ans. A = 2 4
1 3
|A| 2 4 = (1 × 4) – (3 × 2) = 4 – 6 = –2 So |A| = –2
1 4 –3 –2 –3/2
–1
A = =
2 –2 1 1 –1/2
1 3 –2 –3/2 1–2 3+3/2 –1 9/2
A + A = 2 4 + 1 –1/2 2+1 4–1/2 3 7/2
–1
4. If A= {1,2,3,4,5} and B = {2,4,6} then using set theory, find A-B.
Ans. A – B is denoted by the set containing elements that are in A but not in B. Hence, A – B = {1,3,5}
5. Give a = (3,1, –5) and b = (0, –2, 4) find the cross product a × b.
Ans. ā = (3, 1, –5) and b = (0, –2, 4)
i j k
a × b = 3 1 –5
0 –2 4
1 –5 3 –5 3 1
= i –2 4 –j 0 4 +k 0 –2
= ((1 × 4) – (–5 × –2)) i – ((3 × 4) – (–5 × 0)) j + ((3 × –2) – (1 × 0)) k
= (4 – 10)i – 12j – 6k
= 6i – 12j – 6k
Practical Questions 339

