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Let $M_1 = \begin{bmatrix} 6 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$, $M_2 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ \\ and $M_3 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 9 \end{bmatrix}$.\\ The set {$M_1, M_2, M_3$} spans the space of 3 X 3 diagonal matrices.\\ Now, $D = \begin{bmatrix} 12 & 0 & 0 \\ 0 & 15 & 0 \\ 0 & 0 & 75 \end{bmatrix}$ can be written as a \\ linear combination of $M_1, M_2$, and $M_3$.\\ That is, $D = a_1M_1 + a_2M_2 + a_3M_3$.\\ Determine $a_1, a_2$ and $a_3$.\\ $a_1 = $\\ $a_2 = $\\ $a_3 = $

          Let $M_1 = \begin{bmatrix} 6 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$, $M_2 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ \\ and $M_3 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 9 \end{bmatrix}$.\\ The set {$M_1, M_2, M_3$} spans the space of 3 X 3 diagonal matrices.\\ Now, $D = \begin{bmatrix} 12 & 0 & 0 \\ 0 & 15 & 0 \\ 0 & 0 & 75 \end{bmatrix}$ can be written as a \\ linear combination of $M_1, M_2$, and $M_3$.\\ That is, $D = a_1M_1 + a_2M_2 + a_3M_3$.\\ Determine $a_1, a_2$ and $a_3$.\\ $a_1 = $\\ $a_2 = $\\ $a_3 = $

Let M1 =
< b m a t r i x >, M2 =
< b m a t r i x >
and M3 =
< b m a t r i x >.
The set M1, M2, M3 spans the space of 3 X 3 diagonal matrices.
Now, D =
< b m a t r i x > can be written as a
linear combination of M1, M2, and M3.
That is, D = a1M1 + a2M2 + a3M3.
Determine a1, a2 and a3.
a1 =
a2 =
a3 =

Added by Kurt S.

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