# NCERT Class 12-Mathematics: Exemplar Chapter –4 Determinants Part 9

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**Question 16:**

Show that the Δ ABC is an isosceles triangle if the determinant

**Answer:**

We have,

i.e.,

Hence, ABC is an isosceles triangle.

**Question 17:**

Find if and show that

**Answer:**

We have,

And

And

Hence proved.

**Question 18:**

If , then find the value of . Using solve the system of linear equations .

**Answer:**

We have,

Now,

Also, we have the system of linear equations as

And

In the form of ,

We know that,