Linear Algebra

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…

Question : what is an invertible matrix? Give examples Solution : Invertible Matrix : A square matrix with non-zero determinant is called non-singular. An invertible matrix is a non singular…

Question : what are singular and non singular matrices? Give examples Solution : Singular Matrix A square matrix whose determinant is zero is called singular. A singular matrix always has…

Question : what is transpose of a matrix? Give examples Solution : Transpose of a Matrix Matrix obtained by interchanging rows and columns of a matrix \(A\) is called transpose…

Question : how to find Product of two matrices? Give examples Solution : Product of two matrices : Product of two matrices \(A, B\) is possible if number of columns…

Question : how to multiply a matrix by a scalar? Explain Solution : Scalar multiplication : When a scalar \(k\) is multiplied with each entry \( a(i, j) \) of…