Question

Reduce the matrix A(given below) to normal form and hence find its rank.
5 3 8
0 1 1
0 1 1
note : the above is a 3x3 matrix ..

Answer 1

Answer:

The rank of the matrix is equal to the number of non-zero rows in the matrix after reducing it to the echelon form

Given matrix

A=

⎣

⎢

⎢

⎡

1

1

1

1

1

1

1

1

1

⎦

⎥

⎥

⎤

R

2

→R

2

−R

1

A=

⎣

⎢

⎢

⎡

1

0

1

1

0

1

1

0

1

⎦

⎥

⎥

⎤

R

3

→R

3

−R

1

A=

⎣

⎢

⎢

⎡

1

0

0

1

0

0

1

0

0

⎦

⎥

⎥

⎤

Hence the non-zero row in the above matrix is 1.

Therefore , rank is 1.

Answer 2

Step-by-step explanation:

(b)

Reduce the matrix A =

























1 – 1 0

1

1

0

8

3

5