need help with this calculas/matrices problem
- Thread starter MDBFS
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Please share your work for part (a) & (b).View attachment 27076
PART C PLEASE
Use Elementary Row Operations to find scalars α, β and γ (not all zero) such that the unit vector [1, 0, 0]T can be written as a linear combination of the three column vectors of the coefficient matrix A.
That means you want to solve the matrix equation that you wrote out in (a), with [MATH]\begin{pmatrix} 3\\ 0\\ 6 \end{pmatrix}[/MATH] being replaced by [MATH]\begin{pmatrix} 1\\ 0\\ 0 \end{pmatrix}[/MATH]Then write out the 'augmented matrix' and use e.r.o. s to get it into reduced echelon form.
In part (c) you are trying to solve:
[MATH]\begin{pmatrix} 1 & 2 &3\\ 1 & 3 & 5\\ 1 & 5 &12\\ \end{pmatrix} \begin{pmatrix} \alpha\\ \beta \\ \gamma \end{pmatrix} = \begin{pmatrix} 1\\ 0 \\ 0 \end{pmatrix}[/MATH]
The augmented matrix you are going to work on is:
\begin{pmatrix}
1 & 2 &3 &1\\
1 & 3 & 5 & 0\\
1 & 5 &12 & 0\\
\end{pmatrix}
The procedure is algorithmic and you can read a description in the attached pdf.
If you want to send your work we can have a look at it.
It'll be easy, don't worry.
[MATH]\begin{pmatrix} 1 & 2 &3\\ 1 & 3 & 5\\ 1 & 5 &12\\ \end{pmatrix} \begin{pmatrix} \alpha\\ \beta \\ \gamma \end{pmatrix} = \begin{pmatrix} 1\\ 0 \\ 0 \end{pmatrix}[/MATH]
The augmented matrix you are going to work on is:
\begin{pmatrix}
1 & 2 &3 &1\\
1 & 3 & 5 & 0\\
1 & 5 &12 & 0\\
\end{pmatrix}
The procedure is algorithmic and you can read a description in the attached pdf.
If you want to send your work we can have a look at it.
It'll be easy, don't worry.
