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2000017703

Level:

In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?

\begin{aligned} 3 x - 4 y & > 6 \\ - 1.5 x + 2 y & < 5 \end{aligned}

\begin{aligned} 3 x - 4 y & < 6 \\ - 1.5 x + 2 y & < 5 \end{aligned}

\begin{aligned} 3 x - 4 y & < 6 \\ - 1.5 x + 2 y & > 5 \end{aligned}

\begin{aligned} 3 x - 4 y & > 6 \\ - 1.5 x + 2 y & > 5 \end{aligned}

2000017702

Level:

In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?

\begin{aligned} 5 x + 8 y & \leq 27 \\ 9 x + 2 y & < - 15 \end{aligned}

\begin{aligned} 5 x + 8 y & < 27 \\ 9 x + 2 y & \leq - 15 \end{aligned}

\begin{aligned} 5 x + 8 y & \geq 27 \\ 9 x + 2 y & > - 15 \end{aligned}

\begin{aligned} 5 x + 8 y & > 27 \\ 9 x + 2 y & \geq - 15 \end{aligned}

2100017701

Level:

Among the pictures below choose the one in which the shaded region corresponds to the solution of the system

\begin{aligned} 5 x - 9 y & \geq - 1 \\ 7 x + 5 y & \leq 18 \end{aligned}

R \times R

2000017610

Level:

For which positive real number

a

is the determinant of the matrix equal to

36

(\begin{matrix} 2 a & 0 & a \\ 0 & 1 & - 1 \\ a & 2 a & 6 \end{matrix})

a = 2

a = 4

a = 6

a = 0

2000017609

Level:

Calculate the determinant of the following matrix:

(\begin{matrix} 1 + \sqrt{5} & 4 - \sqrt{3} \\ 4 + \sqrt{3} & 1 - \sqrt{5} \end{matrix})

- 17

9

- 23

17

2000017608

Level:

Calculate the determinant of the following matrix:

(\begin{matrix} 7 & 6 & 1 \\ 3 & 2 & 1 \\ 2 & 7 & - 1 \end{matrix})

- 16

12

54

- 52

2000017607

Level:

For which real number

x

is the determinant of the matrix equal to

124

(\begin{matrix} 2^{2} & \sqrt{625} & \sin (- \frac{π}{2}) \\ \log_{3} x & 0 & \cos 0 \\ 2 & 7^{- 1} & - 1 \end{matrix})

27

\frac{1}{27}

9

\frac{1}{9}

2000017606

Level:

Determine the set of all real numbers

b

for which the determinant of the following matrix equals to

5

(\begin{matrix} 4 & b & - 1 \\ 3 & 0 & 2 \\ b & 0 & - 1 \end{matrix})

{1; - \frac{5}{2}}

{- \frac{5}{2}}

{1}

\emptyset

2000017605

Level:

Let

a

and

b

be real numbers. What is the determinant of the following matrix equal to?

(\begin{matrix} a + b & 1 & 0 \\ 1 & a - b & 1 \\ a & 0 & - 1 \end{matrix})

b^{2} - a^{2} + a + 1

a^{2} - b^{2} + a + 1

a^{2} - b^{2} + a - 1

b^{2} - a^{2} - a + 1

2000017604

Level:

Which of the given matrices

A

B

C

and

D

has a different determinant than the others?

A = (\begin{matrix} 6 & 11 \\ 2 & 2 \end{matrix})

B = (\begin{matrix} 1 & 3 \\ 5 & 2 \end{matrix})

C = (\begin{matrix} 5 & - 2 \\ 10 & - 6 \end{matrix})

D = (\begin{matrix} 10 & 0 \\ - 7 & - 1 \end{matrix})

B

D

All given matrices have the same determinant.

Each matrix has a different determinant.

C

2000017703

2000017702

2100017701

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2000017607

2000017606

2000017605

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