(5/4 + -1/2) + -3/2 = 5/4 + (-1/2 + -3/2
Answers
Answer:
5/4 + 1/2
ANSWER
(i)
∣
∣
∣
∣
∣
∣
∣
∣
3
0
3
−1
0
−5
−2
−1
0
∣
∣
∣
∣
∣
∣
∣
∣
Expanding along R
1
Δ=a
11
C
11
+a
12
C
12
+a
13
C
13
=3(−1)
1+1
∣
∣
∣
∣
∣
∣
0
−5
−1
0
∣
∣
∣
∣
∣
∣
−1(−1)
1+2
∣
∣
∣
∣
∣
∣
0
3
−1
0
∣
∣
∣
∣
∣
∣
−2(−1)
1+3
∣
∣
∣
∣
∣
∣
0
3
0
−5
∣
∣
∣
∣
∣
∣
=3(0−5)+1(0+3)−2(0−0)
=−15+3
⇒Δ=−12
(ii)
∣
∣
∣
∣
∣
∣
∣
∣
3
1
2
−4
1
3
5
−2
1
∣
∣
∣
∣
∣
∣
∣
∣
Expanding along R
1
Δ=3(−1)
1+1
∣
∣
∣
∣
∣
∣
1
3
−2
1
∣
∣
∣
∣
∣
∣
−4(−1)
1+2
∣
∣
∣
∣
∣
∣
1
2
−2
1
∣
∣
∣
∣
∣
∣
+5(−1)
1+3
∣
∣
∣
∣
∣
∣
1
2
1
3
∣
∣
∣
∣
∣
∣
Δ=3(1+6)+4(1+4)+5(3−2)
⇒Δ=21+20+5
⇒Δ=46
(iii)
∣
∣
∣
∣
∣
∣
∣
∣
0
−1
−2
1
0
3
2
−3
0
∣
∣
∣
∣
∣
∣
∣
∣
Expanding along R
1
Δ=0(−1)
1+1
∣
∣
∣
∣
∣
∣
0
3
−3
0
∣
∣
∣
∣
∣
∣
+1(−1)
1+2
∣
∣
∣
∣
∣
∣
−1
−2
−3
0
∣
∣
∣
∣
∣
∣
+2(−1)
1+3
∣
∣
∣
∣
∣
∣
−1
−2
0
3
∣
∣
∣
∣
∣
∣
Δ=0−1(0−6)+2(−3−0)
⇒Δ=0+6−6
⇒Δ=0
(iv)
∣
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∣
∣
∣
∣
∣
∣
2
0
3
−1
2
−5
−2
−1
0
∣
∣
∣
∣
∣
∣
∣
∣
Expanding along R
1
Δ=2(−1)
1+1
∣
∣
∣
∣
∣
∣
2
−5
−1
0
∣
∣
∣
∣
∣
∣
−1(−1)
1+2
∣
∣
∣
∣
∣
∣
0
3
−1
0
∣
∣
∣
∣
∣
∣
−2(−1)
1+3
∣
∣
∣
∣
∣
∣
0
3
2
−5
∣
∣
∣
∣
∣
∣
Δ=2(0−5)+1(0+3)−2(0−6)
⇒Δ=−10+3+12
⇒Δ=5
Step-by-step explanation: