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Case II:
A - 1 does not exist But if (adj A) B = 0, then the system is consistent with infinite number of solutions or has no solution. the system is inconsistent i.e., it has no solutio..
A - 1 does not exist But if (adj A) B = 0, then the system is consistent with infinite number of solutions or has no solution. the system is inconsistent i.e., it has no solutio..Determinants
Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denot..
Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denot..Example:
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represents the ele..
(i) Note that the entries in a given matrix need not be distinct. (ii) The entries in this matrix are function of x. A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements. In general, an mxn matrix is in the form Where a i j represents the ele..Addition of Matrices
If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..
If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..Verification by numerical problems
then show that (A+B)+C = A+(B..
then show that (A+B)+C = A+(B..Suggested answer:
From (1) and (2), (A + B) + C = A + (B + C) \ The associative law is verifi..
From (1) and (2), (A + B) + C = A + (B + C) \ The associative law is verifi..
Skew-Symmetric Matrix:
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. ..
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. ..Column Matrix
A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..
A matrix having only one column is called a column matrix. 3 x 1 and 4 x 1 respectivel..See what our Users say :
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