Class 12 Maths - MAHARASHTRA
Matrices
The Matrices chapter in Class 12 Maharashtra State Board (MSBSHSE) mathematics builds upon the basics learned in Class 11. It introduces advanced concepts such as elementary transformations, the inverse of a matrix using both adjoint and elementary row/column operations, and solving systems of linear equations through inversion and reduction methods. This chapter is vital for board exams as it consistently features high-weightage questions, particularly 4-mark and 6-mark application-based problems on solving simultaneous linear equations, making it a high-scoring area for students aiming for top percentages.
Start Learning FreeKey Concepts
Elementary Transformations
Operations performed on the rows or columns of a matrix to simplify it without changing its determinant properties or solution set.
Inverse of a Matrix
A square matrix A has an inverse denoted as A inverse if there exists a matrix B such that AB = BA = I, provided A is a non-singular matrix.
Adjoint of a Matrix
The transpose of the cofactor matrix of a given square matrix, used extensively in finding the inverse of the matrix.
Method of Inversion
A matrix method used to solve a system of linear equations by expressing them as AX = B and finding X = A inverse * B.
Method of Reduction
A technique to solve linear equations by converting the coefficient matrix into an upper triangular matrix using elementary row transformations.
Important Formulas
Board Exam Info
In the Maharashtra (MSBSHSE) Class 12 Mathematics board exam, the Matrices chapter typically carries around 4 to 6 marks without options, and up to 8 marks with options. Common question types include finding the inverse of a 3x3 matrix using adjoint or elementary transformations, and solving a system of three linear equations using either the inversion or reduction method.
Frequently Asked Questions
What is the difference between the inversion method and the reduction method?
The inversion method requires you to explicitly find the inverse of the coefficient matrix using the formula X = A inverse * B. The reduction method uses row transformations to convert the augmented matrix into an upper triangular form to solve for variables directly without calculating the full inverse.
How can I check if my answer for the inverse of a matrix is correct?
You can multiply your calculated inverse matrix with the original matrix (A * A inverse). If the result is the Identity matrix (I), your answer is correct.
Are elementary column transformations allowed when finding the inverse using row operations?
No, if you start using row transformations (elementary row operations) to find the inverse, you must stick strictly to row operations throughout the entire problem. Mixing row and column operations will give an incorrect result.
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