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write the augmented matrix for each system of equations. 10x=10 -5x-8y=9​

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kudzordzifrancis

ANSWER

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

EXPLANATION

The given system of equations is

10x=10

-5x-8y=9

We can rewrite this as:

10x+0y=10

-5x-8y=9

The augmented matrix is the combination of the coefficient matrix and the constant matrix.

The coefficient matrix is

[tex] \left[ { \begin {array} {cc} 10&0\\ - 5& - 8\\ \end {array}} \right] [/tex]

The constant matrix is

[tex] \binom{10}{9} [/tex]

The augmented matrix is

[tex]\left[ { \begin {array} {cc} 10&0& | 10\\-5&-8& | 9\\ \end {array}} \right] [/tex]

Answer:

The augmented matrix is:

         [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]

Step-by-step explanation:

The steps of an augmented matrix are as follows:

  • We write a matrix such that the first column of the matrix is coefficient of x in the matrix.
  • The second column of the matrix is the coefficient of y in each equations.
  • and then it is separated by a line and then the third column written with the help of a constant term on the right side of the equation when it is written down.

The system of equation is:

[tex]10x=10\\and\\-5x-8y=9[/tex]

Hence, the system could be written in the form:

[tex]AX=b[/tex]

where:

[tex]A=\left[\begin{array}{ccc}10&0\\-5&-8\end{array}\right][/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

and

[tex]b=\left[\begin{array}{ccc}10\\9\end{array}\right][/tex]

Hence, the augmented matrix  is:

    [tex]\begin{bmatrix}10 & 0| & 10\\ -5 &-8| & 9\end{bmatrix}[/tex]