school of mathematics

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can be multiplied by usin..

A square matrix A = [a i j ] is said to be skew-symmetric if the (i,j) t h element of A is the negative of the (j,i) t h element of A i.e., if a i j = -a j i for all i, j. In particular, for i = j, we have Thus the diagonal elements of a skew symmetric matrix are all zero. ..

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A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..

The matrices are scalar matrices of order 2 and 3 respectivel..

are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectivel..

We are to select 4 students from 32. This selection can done i..

C(n,r) is the required combination by definition. Each of these combinations consists of a group of r dissimilar things, which can be arranged among themselves in P(r,r) = r! ways. But the number of permutations of n different things taken r at a time is P(n,r)..

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1. O!= 1 2. When n is a negative or fraction, n! is not defined...