# Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations begin{cases}9x-3y+z=13 12x-8z=5 3x+4y-z =6 end{cases}

Question
Forms of linear equations
Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations $$\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases}$$

2021-02-26
For a system of equations $$\begin{cases}ax+by+cz=j \\ dx+ey+fz=k \\ gx+hy+iz =l \end{cases}$$
, the coefficient matrix is $$\begin{bmatrix} a&b&c \\ d&e&f\\ g&h&i \end{bmatrix}$$ and the augmented matrix is $$\begin{bmatrix}a&b&c&j\\ d&e&f&k\\ g&h&i&l \end{bmatrix}$$
a) For the system $$\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases} a=9 ,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4 and i=-1$$ so the coefficient matrix is $$\begin{bmatrix}9&-3&1\\ 12&0&-8\\ 3&4&-1 \end{bmatrix}$$
b) For the system $$\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases} a=9 ,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4 , i=-1 , j=13, k=5 and l=6$$ so the coefficient matrix is $$\begin{bmatrix}9&-3&1\\ 12&0&-8\\ 3&4&-1 \end{bmatrix}$$ so the augmented matrix is $$\begin{bmatrix}9&-3&1&13\\ 12&0&-8&5\\ 3&4&-1&6 \end{bmatrix}$$

### Relevant Questions

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. $$\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases}$$

Let B be a $$(4\times3)(4\times3)$$ matrix in reduced echelon form.

a) If B has three nonzero rows, then determine the form of B.

b) Suppose that a system of 4 linear equations in 2 unknowns has augmented matrix A, where A is a $$(4\times3)(4\times3)$$ matrix row equivalent to B.

Demonstrate that the system of equations is inconsistent.

The coefficient matrix for a system of linear differential equations of the form $$y^1=Ay$$  has the given eigenvalues and eigenspace bases. Find the general solution for the system

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$$\lambda2=0\Rightarrow \begin{bmatrix} 1 \\ 5 \\ 1 \end{bmatrix}\begin{bmatrix}2 \\ 1 \\ 4 \end{bmatrix}$$

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(x,y,z)=()

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations.
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Multiply the coordinates $$x \cdot y$$

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$$3x+7y-20z=-4$$
$$5x+12y-34z=-7$$

The coefficient matrix for a system of linear differential equations of the form $$\displaystyle{y}^{{{1}}}={A}_{{{y}}}$$ has the given eigenvalues and eigenspace bases. Find the general solution for the system.
$$\left[\lambda_{1}=-1\Rightarrow\left\{\begin{bmatrix}1 0 3 \end{bmatrix}\right\},\lambda_{2}=3i\Rightarrow\left\{\begin{bmatrix}2-i 1+i 7i \end{bmatrix}\right\},\lambda_3=-3i\Rightarrow\left\{\begin{bmatrix}2+i 1-i -7i \end{bmatrix}\right\}\right]$$
$$\displaystyle{\left[\begin{matrix}{1}&{0}&-{1}&-{2}\\{0}&{1}&{2}&{3}\end{matrix}\right]}$$
$$\displaystyle{\left[\begin{matrix}{1}&-{1}&{0}&-{2}&{0}&{0}\\{0}&{0}&{1}&{2}&{0}&{0}\\{0}&{0}&{0}&{0}&{1}&{0}\end{matrix}\right]}$$