Khan exercises Maths Tools 1

Matrix with given Eigenvalues

New Numbers

Determine the entry b{\color{red}b} in (612522811263b361194), \begin{pmatrix} -6 & 12 & 5 & -2 \\ -2 & -8 & 11 & -2 \\ -6 & 3 & {\color{red}b} & 3 \\ 6 & 11 & -9 & 4 \end{pmatrix},

such that the matrix has eigenvalues λ1=3\color{blue} \lambda_1 = -3, λ2=7\color{blue} \lambda_2 = -7 λ3=11\color{blue} \lambda_3 = 11 and λ4=9\color{blue} \lambda_4 = -9.