Factor these symmetric, matrices into A = LDL^T. The pivot matrix D is diagonal: A = [ 1 3 3 2 ] and A = [ 1 b b c ] and A = [ 2 -1 0 -1 2 -1 0 -1 2 ].

Question

Factor these symmetric, matrices into A = LD{L}^{T}. The pivot matrix D is diagonal: A =\begin{bmatrix} 1 & 3 \ 3 & 2 \end{bmatrix} and A =\begin{bmatrix} 1 & b \ b & c \end{bmatrix} and A =\left[ \begin{matrix} 2 & -1 & 0 \ -1 & 2 & -1 \ 0 & -1 & 2 \end{matrix} ight].

Accepted Answer

[latex]\begin{bmatrix} 1 & 3 \ 3 & 2 \end{bmatrix}=\begin{bmatrix} 1 & 0 \ 3 & 1 \end{bmatrix}\begin{bmatrix} 1 & 0 \ 0 & -7 \end{bmatrix}\begin{bmatrix} 1 & 3 \ 0 & 1 \end{bmatrix}[/latex];

[latex]\begin{bmatrix} 1 & b \ b & c \end{bmatrix}=\begin{bmatrix} 1 & 0 \ b & 1 \end{bmatrix}\begin{bmatrix} 1 & 0 \ 0 & c-{ b }^{ 2 } \end{bmatrix}\begin{bmatrix} 1 & b \ 0 & 1 \end{bmatrix}[/latex]

[latex]\left[ \begin{matrix} 2 & -1 & 0 \ -1 & 2 & -1 \ 0 & -1 & 2 \end{matrix} ight]=\left[ \begin{matrix} 1 & & \ -\frac { 1 }{ 2 } & 1 & \ 0 & -\frac { 2 }{ 3 } & 1 \end{matrix} ight] \left[ \begin{matrix} 2 & & \ & \frac { 3 }{ 2 } & \ & & \frac { 4 }{ 3 } \end{matrix} ight] \left[ \begin{matrix} 1 & -\frac { 1 }{ 2 } & 0 \ & 1 & -\frac { 2 }{ 3 } \ & & 1 \end{matrix} ight] = LD{L}^{T}[/latex].

Question 2.7.20: Factor these symmetric, matrices into A = LDL^T. The pivot m...

Related Answered Questions