# Matrix Inversion Questions and Answers – Cramer’s Rule

This set of Numerical Methods Multiple Choice Questions & Answers (MCQs) focuses on “Cramer’s Rule”.

### MCQs based on Cramer’s Rule:

1. Cramer’s Rule fails for ___________
a) Determinant > 0
b) Determinant < 0
c) Determinant = 0
d) Determinant = non-real

2. Cramer’s Rule is not suitable for which type of problems?
a) Small systems with 4 unknowns
b) Systems with 2 unknowns
c) Large systems
d) Systems with 3 unknowns

3. Apply Cramer’s rule to solve the following equations.

```3x + y + 2z = 3
2x – 3y –z = -3
X +2y +z = 4```

a) X = 1, y = 2, z = -1
b) X = 2, y = 1, z = -1
c) X = 2, y = -1, z = 1
d) X = 1, y = -1, z = 2

4. Apply Cramer’s rule to solve the following equations.

```x + 3y + 6z = 2
3x – y + z = 9
X – 4y + 2z = 7```

a) X = 1, y = 2, z = -1
b) X = 2, y = – 1, z = -0.5
c) X = 1, y = 2, z = -0.5
d) X = 2, y = 2, z = -1

5. Apply Cramer’s rule to solve the following equations.

```x + y + z = 6.6
x – y + z = 2.2
x + 2y + 3z = 15.2```

a) x = 1.5, y = 2.2, z = -0.5
b) x = 1.5, y = 2.2, z = -0.5
c) x = 1.2, y = 2, z = 3.2
d) x = 1.2, y = 2.2, z = -3.2

6. Apply Cramer’s rule to solve the following equations.

```x + y + z =3
x + 2y + 3z = 4
x + 4y + 9z = 1```

a) x = -0.5, y = 6, z = -2.5
b) x = -0.5, y = 4, z = -2.5
c) x = 4.5, y = 6, z = 1
d) x = 4.5, y = 6, z = 2

7. Apply Cramer’s rule to solve the following equations.

```2x – y + z = 3
3x + 2y + 4z = 19
6x + 7y – z = 17```

a) X = 0.456, y = 1.5442, z = 3.154
b) X = 0.437, y = 1.5312, z = 3.656
c) X = 0.356, y =2.547, z = 5.474
d) X = 0.356, y = 1.722, z = 9.424

8. Apply Cramer’s rule to solve the following equations.

```3x + y + z = 8
2x – 3y -2z = -5
7x + 2y – 5z = 0```

a) X = 1, y =4, z = 2.5
b) X = 4.562, y =4, z = 3.1
c) X = 0.2179, y =1, z = 2.5
d) X = 4.2, y =4, z = 3.145

9. Apply Cramer’s rule to solve the following equations.

```2x + y + z = 10
3x + 2y + 3z = 18
X + 4y +9z = 16```

a) X = -9, y = 1, z = 5
b) X = 7, y = -9, z = 5
c) X = 7, y = 1, z = 5
d) X = 9, y = 1, z = 3

10. Apply Cramer’s rule to solve the following equations.

```2x – y + 3z = 9
x + y + z = 6
x – y + z = 2```

a) x = 1, y = 2, z = 3
b) x = 2, y = 2, z = 3
c) x = 2, y = 3, z = 7
d) x = 1, y = 3, z = 8