class 9th math 1.1 solution

Question#1: Find the order of the following matrices. Solution: \[\begin{align}& \text{Matrix}\qquad &|\qquad &\text{Order} \\ & A=\left[ \begin{matrix}   2 & 3  \\   -5 & 6  \\\end{matrix} \right]\qquad &|\qquad &2-by-2 \\ & B=\left[ \begin{matrix}   2 & 0  \\   3 & 5  \\\end{matrix} \right]\qquad &|\qquad &2-by-2 \\ & C=\left[ \begin{matrix}   2 & 4  \\\end{matrix} \right]\qquad &|\qquad &1-by-2 \\ & D=\left[ \begin{matrix}   4  … Read more

class 9th math 1.2 solution

Question#1: From the following matrices, identify unit matrices, row matrices, column matrices, and null matrices. Solution: \[\begin{align} & A=\left[ \begin{matrix}  0 & 0  \\   0 & 0  \\\end{matrix} \right] \qquad && \text{ Null Matrix} \\ & B=\left[ \begin{matrix}   2 & 3 & 4  \\\end{matrix} \right] \qquad && \text{ Row Matrix} \\ & C=\left[ \begin{matrix}   4  \\   0  \\   … Read more

class 9th math 1.3 solution

Question#1: Which of the following are conformable for addition? Solution: \[\begin{align}& A=\left[ \begin{matrix}   2 & 1  \\   -1 & 3  \\\end{matrix} \right],B=\left[ \begin{matrix}   3  \\   1  \\\end{matrix} \right],C=\left[ \begin{matrix}   1 & 0  \\   2 & -1  \\   1 & -2  \\\end{matrix} \right] \\ & D=\left[ \begin{matrix}   2+1  \\   3  \\\end{matrix} \right],E=\left[ \begin{matrix}   -1 & 0  \\   … Read more

class 9th math 1.4 solution

Question#1: Which of the following product of matrices is conformable for multiplications? \(i\) \[\left[ \begin{matrix}  1 & -1  \\   0 & 2  \\\end{matrix} \right]\left[ \begin{matrix}   -2  \\   3  \\\end{matrix} \right]\] Solution: \[\begin{align}\left[ \begin{matrix}  1 & -1  \\   0 & 2  \\\end{matrix} \right]\left[ \begin{matrix}   -2  \\   3  \\\end{matrix} \right]\\\text{Order of first Matrix}&=2-by-\bbox[5px, border: 1px solid red]{2} … Read more

class 9th math 1.5 solution

Question#1: Find the determinant of the following matrices. \(i\) \[A=\left[ \begin{matrix}   -1 & 1  \\   2 & 0  \\\end{matrix} \right]\] Solution: \[\begin{align}  \left| A \right|&=\left| \begin{matrix}   -1 & 1  \\   2 & 0  \\\end{matrix} \right| \\ & =\left( -1 \right)\left( 0 \right)-\left(1 \right)\left( 2 \right) \\ & =0-2 \\ & =-2 \\  \end{align}\] \(ii\) \[B=\left[ \begin{matrix}   1 & 3  … Read more

class 9th math 1.6 solution

Question#1: Use matrices, if possible to solve the following systems of linear equations.(i) Inversion Method (ii) Cramer’s Rule \(i\) \[\begin{align} & 2x-2y=4 \\ & 3x+2y=6 \\\end{align}\] Solution: Inversion Method: \[\begin{align}   A&=\left[ \begin{matrix}   2 & -2  \\   3 & 2  \\\end{matrix} \right],\;b=\left[ \begin{matrix}   4  \\   6  \\\end{matrix} \right],\;X=\left[ \begin{matrix}   x  \\   y  \\\end{matrix} \right] \\  \left| A \right|&=\left| \begin{matrix}   … Read more

9th class general math exercise 1.1 Urdu Q1 Solution

سوال نمبر۱- درج زیل فی صد کو کسروں کی آسان شکلوں میں واضح کیجئے۔ \((i)\: 95\%\) \[\frac{95}{100}\] سے کاٹیں گے۔\(5\) \[\frac{\cancelto{19}{95}}{\cancelto{20}{100}}\] \[\frac{19}{20}\] \((ii)\,65\%\) \[\frac{65}{100}\] سے کاٹیں گے۔\(5\) \[\frac{\cancelto{13}{65}}{\cancelto{20}{100}}\] \[\frac{13}{20}\] \((iii)\,75\%\) \[\frac{75}{100}\] سے دو بارکاٹیں گے۔\(5\) \[\frac{\cancelto{15}{75}}{\cancelto{20}{100}}\] \[\frac{\cancelto{3}{15}}{\cancelto{4}{20}}\] \[\frac{3}{4}\] \((iv)\,25\%\) \[\frac{25}{100}\] سے دو بارکاٹیں گے۔\(5\) \[\frac{\cancelto{5}{25}}{\cancelto{20}{100}}\] \[\frac{\cancelto{1}{5}}{\cancelto{4}{20}}\] \[\frac{1}{4}\] \((v)\,56\%\) \[\frac{56}{100}\] سے دو بارکاٹیں گے۔\(2\) \[\frac{\cancelto{28}{56}}{\cancelto{50}{100}}\] \[\frac{\cancelto{14}{28}}{\cancelto{25}{50}}\] … Read more