Let A = (habe such that det (A) = 4. Suppose ba; = 24+) 0:; (1 Si, j < 3) and let B = (baj) 3x3, then det(B) is equal to
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Answer:
Given, [P]=a
ij
is a order 3 matrix.
Let Q=
⎣
⎢
⎢
⎡
2
2
a
11
2
3
a
21
2
4
a
31
2
3
a
12
2
4
a
22
2
5
a
32
2
4
a
13
2
5
a
23
2
6
a
33
⎦
⎥
⎥
⎤
∣Q∣=
∣
∣
∣
∣
∣
∣
∣
∣
2
2
a
11
2
3
a
21
2
4
a
31
2
3
a
12
2
4
a
22
2
5
a
32
2
4
a
13
2
5
a
23
2
6
a
33
∣
∣
∣
∣
∣
∣
∣
∣
⇒Q=2
2
2
3
2
4
⎣
⎢
⎢
⎡
a
11
2a
21
2
2
a
31
a
12
2a
22
2
2
a
32
a
13
2a
23
2
2
a
33
⎦
⎥
⎥
⎤
⇒∣Q∣=2
9
×2×2
2
∣
∣
∣
∣
∣
∣
∣
∣
a
11
a
21
a
31
a
12
a
22
a
32
a
13
a
23
a
33
∣
∣
∣
∣
∣
∣
∣
∣
⇒∣Q∣=2
12
∣P∣
⇒∣Q∣=2
13
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