Question

Matrices
9 이
120
P and Q are non-singular such that PAQ =
Hence the rank of A = 2.
0 0
Note : P and 2 obtained in the above problem are not unique.
Example 2 : , Find the non-singular matrices P and Q such that PAQ is in normal form,
13 2 -1 5
[JNTU (K) May 2016 (Set No. 2)]
where A = 5 1 4
1 4 11 -19​

Answer 1

Answer:

So, we start with:

⎡⎣⎢1232−20314−231⎤⎦⎥[123−22−2133041] = ⎡⎣⎢100010001⎤⎦⎥A⎡⎣⎢⎢⎢1000010000100001⎤⎦⎥⎥⎥[100010001]A[1000010000100001]

and after performing the operations outlined above, end up with: