The determinant of a 2x2 matrixA=(abcd)is calculated using the formula: det(A)=ad−bc For our matrixA: -a=2 -b=3 -c=4 -d=5 Thus, the determinant is: det(A)=(2)(5)−(3)(4)=10−12=−2 Step 2: Find the Adjoint of A ...
Inverse matrix can be calculated using different methods. Learn what is inverse matrix, how to find the inverse matrix for 2x2 and 3x3 matrices along with the steps and solved examples here at BYJU'S.
To solve the problem, we need to find the adjoint of the matrix A and then verify that A⋅(adjA)=(adjA)⋅A=|A|⋅I. Given:A=⎛⎜⎝−1−2−221−22−21⎞⎟⎠ Step 1: Calculate the Determinant of Matrix A We will calculate the determinant of A using the for...
The eigenvalues of a matrix are the scalars by which eigenvectors change when some transformation is applied to them. Learn how to find the eigenvalues of 2x2 and 3x3 matrices using the characteristic equation with examples.
The another name of the vector space is the eigenspace. The eigenvalue and the eigenvector of the matrix are to be determined if we are asked to analyze the various characteristics of the matrix.Answer and Explanation: To find a basis for an eigenspace of the Matrix A, we first have to...
If MatrixA=[B+C+D+E]. What isA−1( The inverse of the matrix) using matrix properties? Matrices: For an×nmatrix, say matrixA, we can find its inverse matrix by dividing the adjoint of the matrix by its determinant. Mathema...
Answer to: Find one nontrivial solution of Ax = 0, where \displaystyle{ A = \left[ \begin{array}{rr} 3 & 2 \\ 6 & 4 \end{array} ...
Find the inverse of A ifA3−3A2+4A=0. Characteristic Equation: A square matrixAhas the same number of eigenvalues as its order. The eigenvalues of the matrix are obtained as the solution of its characteristic equation. The Cayley-Hamilton theorem ensures that the given matrix also satisfies ...
To solve the problem, we need to find the value of BA+2I, where A=(1−125), B=(−2231), and I is the identity matrix. Step 1: Calculate the product BA To find BA, we multiply matrix B with matrix A: BA=(−2231)(1−125) Using matrix multiplication, the element at pos...
Find the adjoint of matrix A = [(2,0,-1),(3,1,2),(-1,1,2)] 04:41 Find the matrix X such that {:((1,2,3),(2,3,2),(1,2,2)):} X = {:((2,2... 08:19 If A=[[sectheta, tantheta, 0], [tantheta, sectheta, 0], [0, 0, 1]], th... 06:44 Transform ...