Determinants — Course Quiz | Expresswala Academy

Evaluate

\begin{vmatrix} 6 & 2 \\ 3 & -1 \end{vmatrix}

.

A

-12

B

12

C

-6

D

0

If two rows of a determinant are identical, its value is

A

1

B unchanged if the rows are swapped, but not necessarily

0

C the square of either row's sum

D

0

If

\lvert A \rvert = -7

, then

\lvert A^T \rvert

is

A

7

B

\displaystyle \tfrac{1}{7}

C

-7

D

49

For which

k

are the points

(1, 2)

,

(3, k)

and

(5, 10)

collinear?

A

8

B

5

C

4

D

6

For

\begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 0 \end{vmatrix}

, the minor

M_{21}

is

A

-24

B

-48

C

-21

D

24

Find the area of the triangle with vertices

(1, 1)

,

(5, 1)

and

(3, 6)

.

A

12

B

20

C

10

D

15

The inverse of

\begin{bmatrix} 2 & 1 \\ 5 & 3 \end{bmatrix}

is

A

\begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix}

B

\begin{bmatrix} 2 & -1 \\ -5 & 3 \end{bmatrix}

C

\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}

D

\begin{bmatrix} -3 & 1 \\ 5 & -2 \end{bmatrix}

If

\lvert A \rvert = 3

and

\lvert B \rvert = -2

for square matrices of the same order, then

\lvert AB \rvert

is

A

\displaystyle -\tfrac{3}{2}

B

-6

C

6

D

1

Solve by the matrix method:

x + y = 4

,

2x - y = 5

.

A

x = 1

,

y = 3

B

x = 3

,

y = 1

C

x = 2

,

y = 2

D

x = 3

,

y = -1

For a system

AX = B

with

\lvert A \rvert = 0

and

(\operatorname{adj}A)B \ne O

, the system

A has no solution

B has a unique solution

C has the solution

X = O

D has infinitely many solutions

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Determinants — Course Quiz

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