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Ch 03: Matrices and Determinants @fsc-part1-ptb:important-questions
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$ if $ \left[ {\begin{array}{c} x+3&1\\ -3& 3y-4 \end{array}} \right]= \left[ {\begin{array}{c} 2&1\\ -3&2 \end{array}} \right]$ --- // BISE Gujrawala(2015)// ... matrix $A$ if $\left[ {\begin{array}{c}4&3\\ 2&2 \end{array}} \right]A-\left[ {\begin{array}{c} 2&3\\ -1&-2 \end{array}} \right]= \left[ {\begin{array}{c} -1&-4\\
Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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ne 0 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline \end{array} \] Answers the questions: (i) Name the id... & 0 & 1 \\ \hline 0 & 3 & 0 & 1 & 2 \\ \hline \end{array} \] **Solution** Suppose $G=\left\{ 0,1,... E & E & O \\ \hline O & O & E \\ \hline \end{array} \] **Solution** As $E + E = E$, $E + O... hline \omega^2 & \omega^2 & 1 & \omega \\ \hline \end{array} \] (i) A table show that all the entries
Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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|c|c|} \hline + & 0 \\ \hline 0 & 0 \\ \hline \end{array} \] As $0+0=0 \in \{0\}$. This implies $\{... } \hline \times & 0 \\ \hline 0 & 0 \\ \hline \end{array} \] As $0\times 0=0 \in \{0\}$ This impli... |c|c|} \hline + & 1 \\ \hline 1 & 2 \\ \hline \end{array} \] As $1+1=2 \notin \{1\}$. This implies... } \hline \times & 1 \\ \hline 1 & 1 \\ \hline \end{array} \] As $1\times 1=1 \in \{1\}$. This implie
Definitions: FSc Part 1 (Mathematics): PTB
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= \left[ {\begin{array}{c} 1&2&3\\ 0&8&4\\ 2&1&1 \end{array}} \right]$ * **Order:** Order of Matri... e.g. $A = \left[ {\begin{array}{c} 3&1&7\\ 0&5&4 \end{array}} \right]$. Order of $A$=$2 \times 3$ * ... Matrix. e.g. $B = \left[ {\begin{array}{c} 1&4&6 \end{array}} \right]$ * **Column matrix:** A matrix... trix. e.g. $B = \left[ {\begin{array}{c} 1\\3\\5 \end{array}} \right]$ * **Square matrix:** A matrix
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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box{In fact if } z=a+bi, \mbox{ then } -z=-a-bi. \end{array}\nonumber\] - Associative Law for Addition ... -(i^2)^{9} \cdot i \\ & =-(-1)^{9} i=-(-1)i =i. \end{align} **Question 4(iv)** Simplify: $\displays... \frac{i}{i}\\ &=\frac{i}{i^2}=\frac{i}{-1}=-i. \end{align} </panel> <panel> **Question 5(i)** Writ... in \mathbb{R}, \text{ as } x,y \in \mathbb{R}. \end{align} Now \begin{align} \text{Product}&=z\cdot
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
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\\ T & F & F \\ F & T & F \\ F & F & F \\ \hline \end{array} \] ====Tautology==== A tautology is a sta
Ch 04: Quadratic Equations @fsc-part1-ptb:important-questions
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// $${\begin{array}{c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array}}$$ * Find the roots of the equation $4
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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Book Board, Lahore. The answers are given at the end of the page. ====MCQs==== - If $*$ is a binary
MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
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Book Board, Lahore. The answers are given at the end of the page. ====MCQs==== - A well defined col
MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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Book Board, Lahore. The answers are given at the end of the page. ====MCQs==== - An equation $ax^2+