Is a matrix is symmetric as well as skew symmetric then?

Is a matrix is symmetric as well as skew symmetric then?

A matrix which is both symmetric as well as skew-symmetric is a null matrix.

Does there exist skew symmetric orthogonal matrix of order 3 * 3?

No, an orthogonal matrix has determinant ±1 whereas a skew symmetric matrix of order 3 has determinant 0.

Can every 3×3 matrix be represented by two vectors?

Only de-generated 3×3 matrices, whose rank < 3, can be represented by 2 vectors.

How do you write a symmetric matrix?

Step 1- Find the transpose of the matrix. Step 2- Check if the transpose of the matrix is equal to the original matrix. Step 3- If the transpose matrix and the original matrix are equal , then the matrix is symmetric.

Is any square matrix then which of the following is skew-symmetric?

For any square matrix write whether AAT is symmetric or skew-symmetric. If A is a square matrix then show that A+AT and AAT are symmetric and A-AT is skew – symmetric. For any square matrix (A-A1)2 is skew symmetric .

Do there exist non diagonal symmetric 3 3 matrix that are orthogonal?

Give an example of two matrices whose product is a 3×2 matrix. A matrix A is called symmetric if AT=A. Verify, for all 3×3… Suppose A is a 3×3 matrix and y is a vector in R3…

Is symmetric matrices a vector space?

I think you mean that the set of all symmetric matrices (of some size) form a vector space—a subspace of the vector space of all matrices of that size. This can be checked by the usual three-point checklist for subspaces: Zero: The zero matrix is symmetric.

What is the difference between symmetric and skew symmetric matrices?

The diagonal elements make the center of the matrix and a symmetric matrix will look the same on either side of the diagonal. This is true for 3×3 matrices as well as any size square matrix. Skew symmetric is a little different, but not by much. On a skew symmetric matrix, the diagonal elements will always be zero.

How do you tell if a matrix is symmetric or asymmetric?

The diagonal elements make the center of the matrix and a symmetric matrix will look the same on either side of the diagonal. This is true for 3×3 matrices as well as any size square matrix. Skew symmetric is a little different, but not by much.

Are the rows of a symmetric matrix always the same?

You could say the rows of a symmetric matrix are always the same as the columns. Another way to see this is to think about “reflecting” the matrix over it’s diagonal. The diagonal elements make the center of the matrix and a symmetric matrix will look the same on either side of the diagonal.

How do you find the product of two symmetric matrices?

If A and B are two symmetric matrices and they follow the commutative property, i.e. AB =BA, then the product of A and B is symmetric. If matrix A is symmetric then A n is also symmetric, where n is an integer. If A is a symmetrix matrix then A -1 is also symmetric.