Matrices and determinants

9000019902

Level:

Find the rank of the following matrix

B

B = (\begin{matrix} 3 & 3 & - 2 & 0 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & - 3 & 0 \end{matrix})

rank (B) = 3

rank (B) = 2

rank (B) = 1

rank (B) = 0

2000017601

Level:

Calculate the determinant of the following matrix:

(\begin{matrix} 3 & 0 & - 1 \\ 2 & 4 & 0 \\ 1 & 1 & 5 \end{matrix})

62

54

66

The result does not belong to the set

{54; 62; 66}

2000017602

Level:

Calculate the determinant of the following matrix:

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

1

3

- 1

The result does not belong to the set

{- 1; 1; 3}

2000017603

Level:

For what value of

a

is the determinant of the following matrix equal to

14

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

a = 5

a = 6

a = 9

The value of

a

does not belong to the set

{5; 6; 9}

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.

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

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

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}

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

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

Matrices and determinants

9000019902

2000017601

2000017602

2000017603

2000017604

2000017605

2000017606

2000017607

2000017608

2000017609

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