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# Common Mistakes Made in ICSE Class 10 Board Exams Chapter Matrices

In the ICSE Class 10 syllabus, Matrices is a chapter from the Algebra unit. To score full marks in this chapter, one has to be well-versed in the rules and types of matrices. However, most of the students get confused in remembering these rules and tend to make mistakes by applying incorrect rules. Even confusion in rows and columns leads to incorrect solutions.

Mistake in writing Correct ORDER of a Matrix

Apart from a clear understanding of the order of a matrix, during exams, students get confused and interchange the order of a matrix.

Order of a Matrix = Number of rows in it × Number of columns in it

But, in a hurry, students interchange the order of rows and columns resulting in the incorrect order of a matrix.

Students think that order 2 × 3 of a matrix is the same as order 3 × 2 of a matrix.

But, this is not true.

Since matrix of order 2 × 3 indicates matrix with 2 rows and 3 columns whereas a matrix of order 3 × 2 indicates a matrix with 3 rows and 2 columns.

Mistake in writing Correct TRANSPOSE of a Matrix

If A is a matrix, then its transpose is obtained by interchanging its rows and columns.

While writing the transpose of a matrix, one needs to interchange rows with columns. But many students either interchange one row with the other row or one column with the other column and get incorrect transpose of a matrix.

The solution involving writing the transpose of a matrix is expected in question related to solving matrix equation. If you take the incorrect transpose of a matrix, the solution of the matrix equation will be wrong.

Mistake Made while writing ADDITIVE INVERSE of a Matrix

The additive inverse of a matrix A is negative of matrix A, that is, –A.

While writing additive inverse of a matrix, the sign of each element in a matrix is changed. But, most of the times, students change only the sign of a positive element in a matrix failing to change the sign of a negative element.

Mistakes in Doing MULTIPLICATION of Matrices

The most common error made by students in answering Matrices questions is related to matrix multiplication. Students generally fail to follow the basic rule of matrix multiplication. The rule for matrix multiplication is stated below.

But, many times, students follow the incorrect rule of matrix multiplication as follows:

Also, students tend to make mistakes in sums wherein we need to find A(B + C), where A, B and C are three matrices.

In the solution, firstly, we need to find (B + C). Once the addition is done, we have to find the product A(B + C). However, many students get the sum (B + C) correct but commit mistakes in finding the product. That is instead of doing A(B + C), they do (B + C)A assuming both are the same.

But, in matrix multiplication A(B + C) ≠ (B + C)A. This will give a different answer which is incorrect.

Also, some students waste their time in finding AB and AC. This is not incorrect but it will take more time to answer the question. And, as we all know, we have to do effective utilization of time during exams, so avoid doing lengthy solutions wherever possible. Hence, finding the sum (B + C) and then calculating A(B + C) is a direct method and will consume less time.

PRACTICE QUESTIONS

Question 1:
If matrix A is of order 3 x 2 and matrix B is of order 2 x 2, then find the order of matrix AB.

Hint: Follow the rule to define the order of a matrix. For a detailed solution,  click here.

Question 2: If A =   and B is a null matrix, find the value of A + 2B + IA.
Hint: All elements in a null matrix are zero. For a detailed solution, click here.

CONCLUSION

By looking at all these mistakes committed by most of the students, each one of you needs to follow the correct rules in Matrices. This will help to score good marks. Hope all these mistakes focused on in this blog prevent you from committing errors in your exams. These mistakes are based on CISCE Pupil Analysis done in a year. At  TopperLearning, we bring you unique e-learning experiences, providing quality resources to students all over the country. You can enhance your concept understanding through Revision Note, Assertion and Reasoning Questions and Videos.

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