Question

Which coefficient matrix represents a system of linear equations that has a unique solution ?
Options in photo*

Answer 1

Answer:

Option C

Step-by-step explanation:

We are given a coefficient matrix along and not the solution matrix

Since solution matrix is not given we cannot check for infinity solutions.

But we can check whether coefficient matrix is 0 or not

If coefficient matrix is zero, the system is inconsistent and hence no solution.

Option A)

|A|=$\left[\begin{array}{ccc}4&2&6\\2&1&3\\-2&3&-4\end{array}\right] =0$

since II row is a multiple of I row

Hence no solution or infinite

OPtion B

|B|=$\left[\begin{array}{ccc}2&0&-2\\-7&1&5\\4&-2&0\end{array}\right] \\=2(10)-2(10)=0$

Hence no solution or infinite

Option C

$\left[\begin{array}{ccc}6&0&-2\\-2&0&6\\1&-2&0\end{array}\right] \\=2(36-2)=68$

Hence there will be a unique solution

Option D

$\left[\begin{array}{ccc}5&10&5\\4&1&4\\-1&-2&-1\end{array}\right] \\=2(10)-2(10)=0$=0

(since I row is -5 times III row)

Hence there will be no or infinite solution

Option C is the correct answer