Given the matrix ( A = begin{bmatrix} 1 & 3 4 & 2 end{bmatrix} ), find the characteristic equation and hence the eigenvalues.

Question

Given the matrix ( A = begin{bmatrix} 1 & 3  4 & 2 end{bmatrix} ), find the characteristic equation and hence the eigenvalues.

Accepted Answer

Step:1 ：The characteristic equation is obtained by setting the determinant of ( (A - lambda I) ) equal to zero, where ( I ) is the identity matrix and ( lambda ) are the eigenvalues. Hence, ( A - lambda I = begin{bmatrix} 1-lambda & 3  4 & 2-lambda end{bmatrix} ).Step:2 ：We then find the determinant of ( A - lambda I ), which is ( (1-lambda)(2-lambda) - (3)(4) = lambda^2 - 3lambda - 10 ).Step:3 ：Setting this equation equal to zero gives the characteristic equation, which is ( lambda^2 - 3lambda - 10 = 0 ).

Answer

Step: 1 ：The characteristic equation is obtained by setting the determinant of ( (A - lambda I) ) equal to zero, where ( I ) is the identity matrix and ( lambda ) are the eigenvalues. Hence, ( A - lambda I = begin{bmatrix} 1-lambda & 3  4 & 2-lambda end{bmatrix} ).Step: 2 ：We then find the determinant of ( A - lambda I ), which is ( (1-lambda)(2-lambda) - (3)(4) = lambda^2 - 3lambda - 10 ).Step: 3 ：Setting this equation equal to zero gives the characteristic equation, which is ( lambda^2 - 3lambda - 10 = 0 ).

Given the matrix $A = [\begin{matrix} 1 & 3 4 & 2 \end{matrix}]$ , find the characteristic equation and hence the eigenvalues.

Answer

Popular Problems

Given the matrix A=[13 42], find the characteristic equation and hence the eigenvalues.

Answer

Popular Problems

Given the matrix $A = [\begin{matrix} 1 & 3 4 & 2 \end{matrix}]$ , find the characteristic equation and hence the eigenvalues.