AKUEB HSSC-I Mathematics Matrices and Determinants MCQs & Practice Questions

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.1 Matrices / 2.1.1

AKU-EB Model Paper 2025MEDIUM

Fill in the following blanks:

Given that

Q'P' = \begin{bmatrix} m & 2 & 0 \\ 3 & 0 & 1 \\ 0 & 4 & 10 \end{bmatrix}

i. State the matrix $PQ$ .

\begin{bmatrix} (1,1) & (1,2) & (1,3) \\ (2,1) & (2,2) & (2,3) \\ (3,1) & (3,2) & (3,3) \end{bmatrix}

Entry (1,1) is
Entry (1,2) is
Entry (1,3) is
Entry (2,1) is
Entry (2,2) is
Entry (2,3) is
Entry (3,1) is
Entry (3,2) is
Entry (3,3) is
ii. Determine the value of $m$ for which the matrix $PQ$ will become singular.

m

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.1 Matrices / 2.1.1

AKU-EB Model Paper 2025MEDIUM

Fill in the following blanks:

For the matrices

A=\begin{bmatrix} i \\ 2i \\ 3i \end{bmatrix}

and

B=\begin{bmatrix} i & 4i \end{bmatrix}

, find

A\times B

and

(A\times B)\times(A\times B)'

.
(Note:

i=\sqrt{-1}

)
Part 1: $A \times B$

\begin{bmatrix} (1,1) & (1,2) \\ (2,1) & (2,2) \\ (3,1) & (3,2) \end{bmatrix}

Entry (1,1) is
Entry (1,2) is
Entry (2,1) is
Entry (2,2) is
Entry (3,1) is
Entry (3,2) is
Part 2: $(A\times B)\times(A\times B)'$

\begin{bmatrix} (1,1) & (1,2) & (1,3) \\ (2,1) & (2,2) & (2,3) \\ (3,1) & (3,2) & (3,3) \end{bmatrix}

Entry (1,1) is
Entry (1,2) is
Entry (1,3) is
Entry (2,1) is
Entry (2,2) is
Entry (2,3) is
Entry (3,1) is
Entry (3,2) is
Entry (3,3) is

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.3 Solution of Linear Equations using Matrices / 2.3.3

AKU-EB Model Paper 2025MEDIUM

Fill in the following blanks:

The matrix form of the system of simultaneous linear equations

x+3y+3z=1

y+2z=2

, and

2x+y=3

is:

\begin{bmatrix}1&3&3\\0&1&2\\2&1&0\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\2\\3\end{bmatrix}

|A|=4

, then find the value of the matrix

\begin{bmatrix}x\\y\\z\end{bmatrix}

using the matrix inversion method.
Note: Answer in fractions like 2/3,4/5.
The value of x is
The value of y is
The value of z is

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.1 Matrices / 2.1.2

AKU-EB Model Paper 2025EASY

Which of the following conditions is TRUE for a periodic matrix $A$ ? (Note: $k>0$ )

kA=I

A^{k+1}=A

A^{k+1}=I

A^k=0

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.2 Determinants of Matrices of Order 3 / 2.2.6

AKU-EB Model Paper 2025MEDIUM

The determinant of the matrix $\begin{bmatrix}a&b&c\\b&a&c\\2a&2b&2c\end{bmatrix}$ is

0

2

abc

2abc

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.2 Determinants of Matrices of Order 3 / 2.2.2

AKU-EB Model Paper 2025EASY

The determinant of the matrix $\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$ will be

-1

0

1

2

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.2 Determinants of Matrices of Order 3 / 2.2.8

AKU-EB Model Paper 2025EASY

The inverse of the matrix $\begin{bmatrix}1&2\\0&1\end{bmatrix}$ is

\begin{bmatrix}1&-2\\0&1\end{bmatrix}

\begin{bmatrix}1&2\\0&1\end{bmatrix}

\begin{bmatrix}-1&2\\0&-1\end{bmatrix}

not possible

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.2 Determinants of Matrices of Order 3 / 2.2.3

AKU-EB Model Paper 2025EASY

The cofactor of the element in the third row and the second column of the matrix $\begin{bmatrix}2&2&3\\1&2&3\\1&5&7\end{bmatrix}$ is

8

3

-3

-8

Class 11 - Mathematics / Unit 2 - Matrices and Determinants / 2.1 Matrices / 2.1.1

AKU-EB Model Paper 2025MEDIUM

The product of the matrices $\begin{bmatrix}-i \\ i^2\end{bmatrix}$ and $\begin{bmatrix}i\\1\end{bmatrix}$ is

[0]

\begin{bmatrix}1\\-1\end{bmatrix}

\begin{bmatrix}-1\\-1\end{bmatrix}

not possible

Matrices and Determinants - HSSC-I Mathematics