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 2.2 solution

Question#1: Identify the property used in the following. \[\begin{align}   \left( \text{i} \right)\qquad&a+b=b+a\qquad &&\text{Commutative Property w}\text{.r}\text{.t}\text{. addition } \\  \left( \text{ii} \right) \qquad &\left( ab \right)c=a\left( bc \right) \qquad &&\text{Associatve Property w}\text{.r}\text{.t}\text{. multiplication} \\  \left( \text{iii} \right) \qquad &7\times 1=7\qquad &&\text{Multiplicative Identity} \\  \left( \text{iv} \right) \qquad &x>y\text{ or }x=y\text{ or }x<y\qquad &&\text{Trichotomy Property} \\  \left( \text{v} \right) \qquad &ab=ba\qquad … Read more

class 9th math 2.3 solution

Question#1: Write each radical expression in exponential notation and each exponential expression in radical notation. Do not simplify. \[\begin{align} (\text{i})\qquad&\sqrt[3]{-64} \\ & ={{\left( -64 \right)}^{\frac{1}{3}}} \\  (\text{ii})\qquad&{{2}^{3/5}} \\ & =\sqrt[5]{{{2}^{3}}} \\  (\text{iii})\qquad&-{{7}^{1/3}} \\ & =\sqrt[3]{-7} \\  (\text{iv})\qquad&{{y}^{-2/3}} \\ & =\sqrt[3]{{{y}^{-2}}} \\\end{align}\] Question#2: Tell whether the following statements are true or false? \[\begin{align}   \left( \text{i} \right) \qquad & {{5}^{1/5}}=\sqrt{5}\qquad & \textbf{False} \\  \left( \text{ii} \right)\qquad … Read more