Linear Algebra

Question : what is Echelon Form of a Matrix? Find Echelon Form of the following Matrix Solution : Echelon Form of a Matrix A matrix is in row echelon form…

Question : what is rank of matrix? Find rank of the following matrix \[\left( {\begin{array}{*{20}{c}}1&{ 2}&{ 3}\\{ 2}&4&{ 6}\\{ 4}&{ 8}&12\end{array}}\right)\] Solution : Rank of Matrix : Rank of Matrix…

Question : what is determinant? Find determinant of the following matrices \[\left(\begin{array}{cc}2 & -1 \\3 & 1 \end{array}\right)\] \[\left(\begin{array}{ccc}1 & -1 & 0 \\1 & 3 & -1 \\3 &…

Question : what are symmetric and skew symmetric matrices ? Give Examples Solution : Symmetric Matrix A matrix \(A\) whose transpose \(tr(A)\) is same as as \(A\) is called symmetric.…

Question : what are triangular matrices ? Give Examples Solution : Triangular Matrix A square matrix \(A=(a_{i,j})_{1 \le i,j \le n}\) whose entries satisfy either \(a_{i,j} =0 \forall i\ge j\)…

Question : What are different types of Matrices ? Give examples Solution : Types of Matrices Some the basic types of matrices are Zero Matrix Zero matrix is matrix will…

Question : what is inverse of a matrix? Find inverse of the matrix [2,3,-1;4,0,5;6,0,-2] Solution : Inverse of Matrix Ratio of \(adj(A)\) to \(det(A)\) is called inverse of \(A\). It…

Question : how do you find Cofactor of Matrix? Solution : Cofactor of Matrix Cofactor of a matrix \(A\) is a matrix \(c_{i,j}\) where \(c_{i,j} =(-1)^{i+j}M_{i,j}\). It is denoted as…

Question : what is Minor of Matrix? Solution: Minor of Matrix .\((i,j)\) minor of a matrix \(A\) is denoted as \(M_{i,j}\) and it is the determinant of submatrix \(S_{i,j}\) of…

Question : how to find sub-matrices of a matrix? Give examples Solution : Sub-matrix of a Matrix Let \(A = \left(a(i,j)\right)_{1\le i, j\le 1}\) be a square matrix of order…