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}

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}

Question
Forms of linear equations
asked 2020-11-10
Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. \(\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases}\)

Answers (1)

2020-11-11

For a system of equations \(\begin{cases}ax+by=j \\ cx+dy=k \end{cases}\) ,the coefficient matrix is \(\begin{bmatrix} a&b \\ c&d \end{bmatrix}\) and the augmented matrix is \(\begin{bmatrix}a&b&j\\ c&d&k \end{bmatrix}\)
a) For the system \(\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases} a=8,b=3,c=3\ and\ d=-9\) so the coefficient matrix is \(\begin{bmatrix}8&3\\ 3&-9 \end{bmatrix}\)
b) For the system \(\begin{cases}8x+3y=25 \\ 3x-9y=12 \end{cases} a=8,b=3,c=3 , d=-9 , j=25\ and\ k=12\) so the augmented matrix is \(\begin{bmatrix}8&3&25\\ 3&-9&12 \end{bmatrix}\)

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