Chapter Study

BCA Semester 1 – Mathematics I – Unit 4: Matrices and Determinats

Comprehensive questions and detailed answers for Unit 4: Matrices and Determinats . Perfect for exam preparation and concept clarity.

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\text{Prove that } \begin{vmatrix} x & x^{2} & 1\\ y & y^{2} & 1\\ z & z^{2} & 1 \end{vmatrix} = (x-y)(y-z)(z-x)

MediumTHEORY5 marks2019(TU FOHSS Final)

Define singular and non-singular matrix. Find the inverse of the matrix A:

A= \begin{bmatrix} 1 & −2& −1\\ 2 &1 & 1\\ 3 &−5 &8 \end{bmatrix}

MediumTHEORY5 marks2020(TU FOHSS Final)

\text{If}\quad A = \begin{pmatrix} 4 & 0 \\ 0 & 5 \end{pmatrix}, \text{find a matrix}\space X \space \text{such that } AX = \begin{pmatrix} 12 \\ 24 \end{pmatrix}.

MediumNumerical5 marks2021(TU FOHSS Final)

Define matrix. If $A = \begin{pmatrix}2 & 0 \\ 1 & 3\end{pmatrix}, \quad B = \begin{pmatrix}-2 & 1 \\ 3 & 2\end{pmatrix},$
show that: $(AB)^T = B^T A^T.$

MediumNumerical5 marks2022(TU FOHSS Final)

Prove that:

\begin{vmatrix}a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{vmatrix} = (a - b)(b - c)(c - a)

MediumNumerical5 marks2022(TU FOHSS Final)

Find the inverse of the matrix:

\begin{pmatrix} 1 & 4 & 1 \\ 3 & 3 & -2 \\ 0 & -4 & 1 \end{pmatrix}

MediumNumerical5 marks2023(TU FOHSS Final)

a) Prove that: $\begin{vmatrix} 1 & a & b & c \\ 1 & b & c & a \\ 1 & c & a & b \end{vmatrix} = (a - b)(b - c)(c - a)$
b) By using the vector method, prove that:

$\cos(A - B) = \cos A \cos B + \sin A \sin B$

HardNumerical10 marks2023(TU FOHSS Final)

Prove that: $\begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} = xyz \left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)$

MediumNumerical5 marks2024(TU FOHSS Final)

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