class 9th math 1.1 solution

Question#1: Find the order of the following matrices.

Solution:

\[\begin{align}
& \text{Matrix}\qquad &|\qquad &\text{Order} \\
 & A=\left[ \begin{matrix}
   2 & 3  \\
   -5 & 6  \\
\end{matrix} \right]\qquad &|\qquad &2-by-2 \\
 & B=\left[ \begin{matrix}
   2 & 0  \\
   3 & 5  \\
\end{matrix} \right]\qquad &|\qquad &2-by-2 \\
 & C=\left[ \begin{matrix}
   2 & 4  \\
\end{matrix} \right]\qquad &|\qquad &1-by-2 \\
 & D=\left[ \begin{matrix}
   4  \\
   0  \\
   6  \\
\end{matrix} \right]\qquad &|\qquad &3-by-1 \\
 & E=\left[ \begin{matrix}
   a & d  \\
   b & e  \\
   e & f  \\
\end{matrix} \right]\qquad &|\qquad &3-by-2 \\
 & F=\left[ 2 \right]\qquad &|\qquad &1-by-1 \\
 & G=\left[ \begin{matrix}
   2 & 3 & 0  \\
   1 & 2 & 3  \\
   2 & 4 & 5  \\
\end{matrix} \right]\qquad &|\qquad &3-by-3 \\
 & H=\left[ \begin{matrix}
   2 & 3 & 4  \\
   1 & 0 & 6  \\
\end{matrix} \right]\qquad &|\qquad &2-by-3 \\
\end{align}\]

Question#2: Which of the following matrices are equal?

Solution:

\[\begin{align}
  & A=\left[ 3 \right],\quad B=\left[ \begin{matrix}
   3 & 5  \\
\end{matrix} \right],\quad C=\left[ 5-2 \right] \\
 & D=\left[ \begin{matrix}
   5 & 3  \\
\end{matrix} \right],\quad E=\left[ \begin{matrix}
   4 & 0  \\
   6 & 2  \\
\end{matrix} \right],\quad F=\left[ \begin{matrix}
   2  \\
   6  \\
\end{matrix} \right] \\
 & G=\left[ \begin{matrix}
   3-1  \\
   3+3  \\
\end{matrix} \right],\quad H=\left[ \begin{matrix}
   4 & 0  \\
   6 & 2  \\
\end{matrix} \right],\quad I=\left[ \begin{matrix}
   3 & 3+2  \\
\end{matrix} \right] \\
 & J=\left[ \begin{matrix}
   2+2 & 2-2  \\
   2+4 & 2+0  \\
\end{matrix} \right] \\
 & A=C,B=I,E=H=J,F=G \\
\end{align}\]

Question#3: Find the value of \(a\), \(b\), \(c\), and \(d\) which satisfy the matrix equation.

\[\left[ \begin{matrix}
a+c & a+2b  \\
   c-1 & 4d-6  \\
\end{matrix} \right]=\left[ \begin{matrix}
   0 & -7  \\
   3 & 2d  \\
\end{matrix} \right]\]

Solution:

\begin{array}{l|l|l|l}
a+c=0 & a+2b=-7 & c-1 =3 & 4d-6=2d \\
& & c =3+1 & 4d-2d=6 \\
\text{putting value of }c& & c =4 & 2d=6 \\
a+4=0 & \text{putting value of }a & & d=\frac{6}{2} \\
a=-4 & -4+2b=-7 & & d=3 \\
& 2b=-7+4 & & \\
& 2b=-3 & & \\
& b=\frac{-3}{2} & & \\
\end{array}

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