Question

(12x + y + z = 26

x-11y = 17
1 x - y + 4z =23

4x +y +z =23
x-11y = 17
x - y +12z- 26

x+y +Z=4
x - y = 11
x - y +z=12

x+y+z = 12
x - y = 11
x-y+Z=4

Which linear system has this matrix of constants? [[12][11][4]

Answer 1

Option D. D has the matrix of constants [[12], [11], [4]].

Explanation:

Step 1:

With the given equations, we can form matrices to represent them.

The coefficients of x, y, and z form a matrix of order 3 ×3, the variables x, y, and z form a matrix of order 1 ×3 and the constants form a matrix of order 1 ×3.

Step 2:

The linear system A is represented as

`\left[\begin{array}{ccc}12&1&1\\1&-11&0\\1&-1&4\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]`
`= \left[\begin{array}{ccc}26\\17\\23\end{array}\right]`.

Step 3:

The linear system B is represented as

`\left[\begin{array}{ccc}4&1&1\\1&-11&0\\1&-1&12\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]`
`= \left[\begin{array}{ccc}23\\17\\26\end{array}\right]`.

Step 4:

The linear system C is represented as

`\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]`
`= \left[\begin{array}{ccc}4\\11\\12\end{array}\right]`.

Step 5:

The linear system D is represented as

`\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]`
`= \left[\begin{array}{ccc}12\\11\\4\end{array}\right]`.

Step 6:

Of the four options, the linear system D has the matrix of constants [[12], [11], [4]]. So the answer is option D. D.