Class 12 Maths Chapter 3 Matrices – Exercise 3.1 NCERT Solutions

Introduction

Exercise 3.1 introduces the basic concepts of matrices. Students learn definitions, types of matrices, equality of matrices, and simple operations. This exercise builds the foundation for advanced topics like matrix algebra, determinants, and applications in linear equations.

Key Concepts

1. Definition of Matrix: A matrix is a rectangular array of numbers arranged in rows and columns.

2. Order of a Matrix: If a matrix has $m$ rows and $n$ columns, its order is $m\times n$.

3. Types of Matrices:

   • Row matrix

   • Column matrix

   • Square matrix

   • Zero matrix

   • Diagonal matrix

   • Identity matrix

4. Equality of Matrices: Two matrices are equal if they have the same order and corresponding elements are equal.

Students Frequently Make Mistakes

• Confusing order of matrix with number of elements.

• Misidentifying row vs column matrices.

• Forgetting that equality requires same order and identical entries.

• Mixing up diagonal and identity matrices.

• Writing elements incorrectly in matrix notation.

NCERT Questions with Step‑by‑Step Solutions (10)

Q1. Write the order of matrix $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right]$. Order = $2\times 3$.

Q2. Write the order of matrix $\left[\begin{array}{cc}7& 8\\ 9& 10\\ 11& 12\end{array}\right]$. Order = $3\times 2$.

Q3. Write the order of matrix $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$. Order = $2\times 2$.

Q4. Identify type of matrix $\left[\begin{array}{cc}5& 0\\ 0& 5\end{array}\right]$. Diagonal matrix.

Q5. Identify type of matrix $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$. Zero matrix.

Q6. Identify type of matrix $\left[\begin{array}{ccc}3& 4& 5\end{array}\right]$. Row matrix.

Q7. Identify type of matrix $\left[\begin{array}{c}6\\ 7\\ 8\end{array}\right]$. Column matrix.

Q8. Identify type of matrix $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$. Identity matrix.

Q9. Check if $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. Yes, both are equal.

Q10. Check if $\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$. No, not equal (last element differs).

FAQs (10)

FAQ1. What is a matrix? Rectangular array of numbers.

FAQ2. What is order of matrix? Number of rows × number of columns.

FAQ3. What is row matrix? Matrix with one row.

FAQ4. What is column matrix? Matrix with one column.

FAQ5. What is square matrix? Matrix with equal rows and columns.

FAQ6. What is zero matrix? Matrix with all elements zero.

FAQ7. What is diagonal matrix? Square matrix with non‑zero diagonal elements, others zero.

FAQ8. What is identity matrix? Diagonal matrix with all diagonal elements = 1.

FAQ9. When are two matrices equal? Same order and identical entries.

FAQ10. Why is Exercise 3.1 important? It builds the foundation for matrix algebra.

Conclusion

Exercise 3.1 has 10 solved questions and 10 FAQs that strengthen your understanding of basic matrix concepts. This is the starting point for mastering matrices in Class 12 Maths.

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