If A is 3 x 3 matrix whose rank is 2 and B is 3 x 3 matriwhose rank is 3, then rank of AB is(a) 1(6) 2(C) 3(d) 5
Answers
Answered by
0
Answer:
a) 1
Step-by-step explanation:
Answered by
0
Answer:
Correct option is
B
2
A=
⎣
⎢
⎢
⎡
1
4
3
2
5
4
3
6
5
⎦
⎥
⎥
⎤
Here, ∣A∣=1−4+3=0
So, rank of matrix <3.
Now, we will reduce into Echelon form,
R
2
→R
2
−4R
1
⎣
⎢
⎢
⎡
1
0
3
2
−3
4
3
−6
5
⎦
⎥
⎥
⎤
R
3
→R
3
−3R
1
⎣
⎢
⎢
⎡
1
0
0
2
−3
−2
3
−6
−4
⎦
⎥
⎥
⎤
R
3
→R
3
−
3
2
R
2
⎣
⎢
⎢
⎡
1
0
0
2
−3
0
3
−6
0
⎦
⎥
⎥
⎤
R
2
→−
3
1
R
2
⎣
⎢
⎢
⎡
1
0
0
2
1
0
3
2
0
⎦
⎥
⎥
⎤
Here, there are 2 non-zero rows in the Echelon form of A.
Hence, rank =2
Similar questions