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The answer is yes, and here's why:
Remember that for the eigenvalues (k) and eigenvectors (v) of a matrix (M) the following holds:
M.v = k*v,
where "." denotes matrix multiplication. This operation is only defined if the number of columns in the first matrix is equal to the number of rows in the second, and the resulting matrix/vector will have as many rows as the first matrix, and as many columns as the second matrix.
For example, if you have a 3 x 2 matrix and multiply with a 2 x 4 matrix, the result will be a 3 x 4 matrix.
Applying this to the eigenvalue problem, where the second matrix is a vector, we see that if the matrix M is m x n and the vector is n x 1, the result will be an m x 1 vector. Clearly, this can never be a scalar multiple of the original vector.
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Definition of inverse matrix?
The inverse of a non-singular, n*n matrix, A Is another n*n matrix, A' such that A*A' = A'*A =I(n), the n*n identity matrix.Singular square matrices do not have inverses, nor do non-square matrices.
What is order of the resultant matrix AB when two matrices are multiplied and the order of the Matrix A is m n order of Matrix B is n p Also state the condition under which two matrices can be mult?
the order is m p and the matrices can be multiplied if and only if the first one (matrix A) has the same number of columns as the second one (matrix B) has rows i.e)is Matrix A has n columns, then Matrix B MUST have n rows.Equal Matrix: Two matrices A=|Aij| and B=|Bij| are said to be equal (A=B) if and only if they have the same order and each elements of one is equal to the corresponding elements of the other. Such as A=|1 2 3|, B=|1 2 3|. Thus two matrices are equal if and only if one is a duplicate of the other.
What does N A mean?
It means non- applicable
Do matrices form an abelian group under multiplication?
More precisely, I think you're asking whether the set of n X n matrices forms an abelian group under multiplication. The answer is no (assuming n>1). For example(1 0)(0 1) = (0 1)(0 0)(0 0) (0 0),but(0 1)(1 0) = (0 0)(0 0)(0 0) (0 0). However, the set of n x n diagonalmatrices does form an Abelian set. This is true regardless of the direction of the diagonality, right-to-left or left-to-right. Note that the resulting matrix will also be diagonal, but always right-to-left.
5 divides n if and only if 5 divides n squared?
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