1.

$\mathrm{If} \mathrm{B} = \left[\begin{array}{ccc}3& 2& 0\\ 2& 4& 0\\ 1& 1& 0\end{array}\right], \mathrm{Then}, \mathrm{what} \mathrm{is} \mathrm{adjoint} \mathrm{of} \mathrm{B} = ?$

• $\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ - 2& - 1& 8\end{array}\right]$

• $\left[\begin{array}{ccc}0& 0& - 2\\ 0& 0& - 1\\ 0& 0& 8\end{array}\right]$

• $\left[\begin{array}{ccc}0& 0& 2\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$

• It does not exist

If A is an identity matrix of order 3, then its inverse (A^{- 1} ) :

• is equal to null matrix

• equal to null A

• equal to null 3A

• does not exist

A is a square matrix of order 3 such that its determinantis 4. What is the determinant of its transpose ?

• 64

• 36

• 32

• 4

Let A and B be (3 x 3) matrices with det(A) = 4 and det(B) = 3. What is det (2AB) equal to ?

• 96

• 72

• 48

• 36

Let A and B be (3 x 3) matrices with det(A) = 4 and det(B) = 3. What is det (3AB^{- 1}) equal to ?

• 12

• 18

• 36

• 48

Which one of the following factors does the expansions of the determinant $\left|\begin{array}{ccc}\mathrm{x}& \mathrm{y}& 3\\ {\mathrm{x}}^2& 5{\mathrm{y}}^3& 9\\ {\mathrm{x}}^3& 10{\mathrm{y}}^5& 27\end{array}\right|$ contain ?

• x - 3

• x - y

• y - 3

• x - 3y

The system of equations

2x + y - 3z = 5,

3x - 2y + 2 = 5 and

 5x - 3y - z = 16

• is inconsistent

• is consistent, with a unique solution

• is consistent, with infinitely many solutions

• has its solution lying along x-axis· in three-dimensional space

What is the determinant of the matrix $\left(\begin{array}{ccc}\mathrm{x}& \mathrm{y}& \mathrm{y} +\mathrm{z}\\ \mathrm{z}& \mathrm{x}& \mathrm{z} + \mathrm{x}\\ \mathrm{y}& \mathrm{z}& \mathrm{x} + \mathrm{y}\end{array}\right) ?$

• (x - y)(y - z)(z - x)

• (x - y)(y - z)

• (y - z)(z - x)

• (z - x)²(x + y + z)

If A, B and C are the angles of a triangle and

$$\begin{gathered} \left|\begin{array}{ccc}1& 1& 1\\ 1 + \sin \left(\mathrm{A}\right)& 1 + \sin \left(\mathrm{B}\right)& 1 + \sin \left(\mathrm{C}\right)\\ \sin \left(\mathrm{A}\right) + {\sin }^2\left(\mathrm{A}\right)& \sin \left(\mathrm{B}\right) + {\sin }^2\left(\mathrm{B}\right)& \sin \left(\mathrm{C}\right) + {\sin }^2\left(\mathrm{C}\right)\end{array}\right| = 0, \\ \mathrm{Then} \mathrm{which} \mathrm{one} \mathrm{of} \mathrm{the} \mathrm{following} \mathrm{correct} ? \end{gathered}$$

• The triangle ABC is isosceles

• The triangle ABC is equilateral

• The triangle ABC is scalene

• No conclusion can be drawn with regard to the nature of the triangle

What is the area of the triangle with vertices

$\left(x_1, \frac{1}{x_1}\right), \left(x_2, \frac{1}{x_2}\right), \left(x_3, \frac{1}{x_3}\right) ?$

• $\left|\left({\mathrm{x}}_1 - {\mathrm{x}}_2\right)\left({\mathrm{x}}_2 - {\mathrm{x}}_3\right)\left({\mathrm{x}}_3 - {\mathrm{x}}_1\right)\right|$

• 0

• $\left|\frac{\left({\mathrm{x}}_1 - {\mathrm{x}}_2\right)\left({\mathrm{x}}_2 - {\mathrm{x}}_3\right)\left({\mathrm{x}}_3 - {\mathrm{x}}_1\right)}{{\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3}\right|$

• $\left|\frac{\left({\mathrm{x}}_1 - {\mathrm{x}}_2\right)\left({\mathrm{x}}_2 - {\mathrm{x}}_3\right)\left({\mathrm{x}}_3 - {\mathrm{x}}_1\right)}{2{\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3}\right|$