Khan exercises Maths Tools 1
Determine the entry b{\color{red}b}b in (−6125−2−2−811−2−63b3611−94), \begin{pmatrix} -6 & 12 & 5 & -2 \\ -2 & -8 & 11 & -2 \\ -6 & 3 & {\color{red}b} & 3 \\ 6 & 11 & -9 & 4 \end{pmatrix}, −6−2−6612−8311511b−9−2−234,
b{\color{red}b}b
(−6125−2−2−811−2−63b3611−94), \begin{pmatrix} -6 & 12 & 5 & -2 \\ -2 & -8 & 11 & -2 \\ -6 & 3 & {\color{red}b} & 3 \\ 6 & 11 & -9 & 4 \end{pmatrix}, −6−2−6612−8311511b−9−2−234,
such that the matrix has eigenvalues λ1=−3\color{blue} \lambda_1 = -3λ1=−3, λ2=−7\color{blue} \lambda_2 = -7λ2=−7 λ3=11\color{blue} \lambda_3 = 11λ3=11 and λ4=−9\color{blue} \lambda_4 = -9λ4=−9.
λ1=−3\color{blue} \lambda_1 = -3λ1=−3
λ2=−7\color{blue} \lambda_2 = -7λ2=−7
λ3=11\color{blue} \lambda_3 = 11λ3=11
λ4=−9\color{blue} \lambda_4 = -9λ4=−9
b=\color{red} b =b=