class 9th math 3.1 solution

Question#1: Express each of the following numbers in scientific notations. Solution: \[\begin{align} & \text{Number  }\qquad &| \qquad &\text{Scientific Notation} \\ & \text{(i) }5700\qquad &| \qquad &5.7\times {{10}^{3}} \\ & \text{(ii) }49800000\qquad &| \qquad &4.9\times {{10}^{7}} \\ & \text{(iii) }96000000\qquad &| \qquad &9.6\times {{10}^{7}} \\ & \text{(iv) 416.9}\qquad &| \qquad &4.169\times {{10}^{2}} \\ & \text{(v) }83000\qquad &| \qquad &8.3\times {{10}^{4}} \\ & \text{(vi) … Read more

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

class 9th math 2.1 solution

Question#1: Identify which of the following are rational and irrational numbers. \[\begin{align}  \left( \text{i} \right)\qquad &\sqrt{3}\qquad &&\text{Irrational number} \\  \left( \text{ii} \right) \qquad &\frac{1}{6}\qquad &&\text{Rational number} \\  \left( \text{iii} \right) \qquad &\pi \qquad &&\text{Irrational number} \\  \left( \text{iv} \right) \qquad &\frac{15}{2}\qquad &&\text{Rational number} \\  \left( \text{v} \right) \qquad &7.25\qquad &&\text{Rational number} \\  \left( \text{vi} \right) \qquad &\sqrt{29}\qquad &&\text{Irrational number} \\\end{align}\] Question#2: … Read more

class 9th math 2.5 solution

Question#01: Evaluate \((i)\) \[{{i}^{7}}\] Solution: \[\begin{align}  & ={{i}^{7}} \\ & ={{i}^{6}}\times i \\ & ={{\left( {{i}^{2}} \right)}^{3}}\times i \\ & ={{\left( -1 \right)}^{3}}\times i \\ & =-1\times i \\ & =-i \\\end{align}\] \((ii)\) \[{{i}^{50}}\] Solution: \[\begin{align}  & ={{i}^{50}} \\ & ={{\left( {{i}^{2}} \right)}^{25}} \\ & ={{\left( -1 \right)}^{25}} \\ & =-1 \\  \end{align}\] \((iii)\) \[{{i}^{12}}\] Solution: \[\begin{align}  & ={{i}^{12}} \\ & ={{\left( {{i}^{2}} \right)}^{6}} … Read more

class 9th math 2.4 solution

Question#1: Use the law of exponents to simplify. \((i)\) \[\frac{{{\left( 243 \right)}^{-\frac{2}{3}}}{{\left( 32 \right)}^{\frac{1}{5}}}}{\sqrt{{{\left( 196 \right)}^{-1}}}}\] Solution: \[\begin{aligned}&=\frac{{{\left( 3^5 \right)}^{-\frac{2}{3}}}{{\left( 2^5 \right)}^{-\frac{1}{5}}}}{\sqrt{{{\left( 14^2 \right)}^{-1}}}}\\&=\frac{{{\left( 3 \right)}^{-\frac{5\times 2}{3}}}\times{{\left( 2^\cancel{5} \right)}^{-\frac{1}{\cancel{5}}}}}{\sqrt{{{\left( 14^{-1} \right)}^{2}}}}\\&=\frac{{{\left( 3 \right)}^{-\frac{10}{3}}}\times{{\left( 2 \right)}^{-1}}}{\sqrt{{{\left( 14^{-1} \right)}^{\cancel{2}}}}}\\&=\frac{{{\left( 3 \right)}^{-\frac{10}{3}}}\times{{ 2}^{-1}}}{{{ 14^{-1}}}}\\&=\frac{14}{{{3}^{\frac{10}{3}}}\times 2}\\&=\frac{\cancelto{7}{14}}{3^{\frac{9}{3}}\times {{3}^{\frac{1}{3}}}\times\cancel{2} }\\&=\frac{7}{3^{\frac{\cancelto{3}{9}}{\cancel{3}}}\times {{3}^{\frac{1}{3}}}}\\&=\frac{7}{{{3}^{3}}\times \sqrt[3]{3}}\\&=\frac{7}{27 \sqrt[3]{3}}\end{aligned}\] \((ii)\) \[\left( 2{{x}^{5}}{{y}^{-4}} \right)\left( -8{{x}^{-3}}{{y}^{2}} \right)\] Solution: \[\begin{aligned}&=\left( … Read more