Q. 645.0( 1 Vote )

# Matrix <img

We are given that,

is symmetric matrix.

We need to find the values of a and b.

We must understand what symmetric matrix is.

A symmetric matrix is a square matrix that is equal to its transpose.

A symmetric matrix A = AT

This means, we need to find the transpose of matrix A.

Let us take transpose of the matrix A.

We know that, the transpose of a matrix is a new matrix whose rows are the columns of the original.

We have,

1st row of matrix A = (0 2b -2)

2nd row of matrix A = (3 1 3)

3rd row of matrix A = (3a 3 -1)

For matrix AT, it will become

1st column of AT = 1st row of A = (0 2b -2)

2nd column of AT = 2nd row of A = (3 1 3)

3rd column of AT = 3rd row of A = (3a 3 -1)

Now, as A = AT.

Substituting the matrices A and AT, we get

We know by the property of matrices,

This implies,

a11 = b11, a12 = b12, a21 = b21 and a22 = b22

Applying this property, we can write

2b = 3 …(i)

-2 = 3a …(ii)

3 = 2b

3a = -2

We can find a and b from equations (i) and (ii).

From equation (i),

2b = 3

From equation (ii),

-2 = 3a

Thus, we get and .

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