Identify the terms and factors of 2xy2 – 3x3 -5x by tree method
Answers
In general a 3×4 matrix is given by,
A=
⎣
⎢
⎢
⎡
a
11
a
21
a
31
a
12
a
22
a
32
a
13
a
23
a
33
a
14
a
24
a
34
⎦
⎥
⎥
⎤
(i)
a
ij
=
2
1
∣−3i+j∣,i=1,2,3andj=1,2,3,4
∴a
11
=
2
1
∣−3×1+1∣=
2
1
∣−3+1∣=
2
1
∣−2∣=
2
2
=1
a
21
=
2
1
∣−3×2+1∣=
2
1
∣−6+1∣=
2
1
∣−5∣=
2
5
a
31
=
2
1
∣−3×3+1∣=
2
1
∣−9+1∣=
2
1
∣−8∣=
2
8
=4
a
12
=
2
1
∣−3×1+2∣=
2
1
∣−3+2∣=
2
1
∣−1∣=
2
1
a
22
=
2
1
∣−3×2+2∣=
2
1
∣−6+2∣=
2
1
∣−4∣=
2
4
=2
a
32
=
2
1
∣−3×3+2∣=
2
1
∣−9+2∣=
2
7
a
23
=
2
1
∣−3×2+3∣=
2
1
∣−6+3∣=
2
1
∣−3∣=
2
3
a
33
=
2
1
∣−3×3+3∣=
2
1
∣−9+3∣=
2
1
∣−6∣=
2
6
=3
a
14
=
2
1
∣−3×1+4∣=
2
1
∣−3+4∣=
2
1
∣1∣=
2
1
a
24
=
2
1
∣−3×2+4∣=
2
1
∣−6+4∣=
2
1
∣−2∣=
2
2
=1
a
34
=
2
1
∣−3×3+4∣=
2
1
∣−9+4∣=
2
1
∣−5∣=
2
5
Therefore, the required matrix is
A=
⎣
⎢
⎢
⎡
1
2
5
4
2
1
2
2
3
0
2
3
3
2
1
1
2
5
⎦
⎥
⎥
⎤
(ii)
a
ij
=2i−j,i=1,2,3andj=1,2,3,4
∴a
11
=2×1−1=2−1=1
a
21
=2×2−1=4−1=3
a
31
=2×3−1=6−1=5
a
12
=2×1−2=2−2=0
a
22
=2×2−2=4−2=2
a
32
=2×3−2=6−2=4
a
13
=2×1−3=2−3=−1
a
23
=2×2−3=4−3=1
a
33
=2×3−3=6−3=3
a
14
=2×1−4=2−4=−2
a
24
=2×2−4=4−4=0
a
34
=2×3−4=6−4=2
Therefore, the required matrix is
A=
⎣
⎢
⎢
⎡
1
3
5
0
2
4
−1
1
3
−2
0
2
⎦
⎥
⎥
⎤