Class 12 Maths Chapter 3 Ncert Solutions

Matrices, fundamental in various branches of mathematics and applications, come in different types, each with unique characteristics. Here’s an overview of some common types of matrices:

1. Row Matrix:

   • Definition: A matrix with a single row and multiple columns.
   • Example: $[�,�,�]$[a,b,c]

2. Column Matrix:

   • Definition: A matrix with a single column and multiple rows.
   • Example: $\left[\begin{array}{c}�\\ �\\ �\end{array}\right]$⎣⎡xyz⎦⎤

3. Square Matrix:

   • Definition: A matrix with an equal number of rows and columns.
   • Example: $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$⎣⎡147258369⎦⎤

4. Zero or Null Matrix:

   • Definition: A matrix where all elements are zero.
   • Example: $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$[0000]

5. Identity or Unit Matrix:

   • Definition: A square matrix with diagonal elements equal to 1 and non-diagonal elements equal to 0.
   • Example: $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$⎣⎡100010001⎦⎤

6. Diagonal Matrix:

   • Definition: A square matrix where all non-diagonal elements are zero.
   • Example: $\left[\begin{array}{ccc}2& 0& 0\\ 0& 5& 0\\ 0& 0& 7\end{array}\right]$⎣⎡200050007⎦⎤

7. Scalar Matrix:

   • Definition: A diagonal matrix where all diagonal elements are equal.
   • Example: $\left[\begin{array}{ccc}�& 0& 0\\ 0& �& 0\\ 0& 0& �\end{array}\right]$⎣⎡k000k000k⎦⎤

8. Symmetric Matrix:

   • Definition: A matrix that is equal to its transpose.
   • Example: $\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 5\\ 3& 5& 6\end{array}\right]$⎣⎡12