Determinants Worksheet Class 12 Mathshave been designed as per the latest pattern for CBSE, NCERT and KVS for Grade 12. Students are always suggested to solve printable worksheets for Mathematics Determinants Grade 12 as they can be really helpful to clear their concepts and improve problem solving skills. We at worksheetsbag.com have provided here free PDF worksheets for students in standard 12 so that you can easily take print of these test sheets and use them daily for practice. All worksheets are easy to download and have been designed by teachers of Class 12 for benefit of students and is available for free download.

## Mathematics Determinants Worksheets for Class 12

We have provided **chapter-wise worksheets for class 12 Mathematics Determinants** which the students can download in Pdf format for free. This is the best collection of Mathematics Determinants standard 12th worksheets with important questions and answers for each grade 12th Mathematics Determinants chapter so that the students are able to properly practice and gain more marks in Class 12 Mathematics Determinants class tests and exams.

### Chapter-wise Class 12 Mathematics Determinants Worksheets Pdf Download

• Determinant of a matrix A [a_{11}] _{1×1} = is given by | a_{11} |= a_{11}

• Determinant of a matrix A

• Determinant of a matrix

is given by (expanding along ( R_{1})

• For any square matrix A, the |A| satisfy following properties.

• |A′| = |A|, where A′ = transpose of A.

• If we interchange any two rows (or columns), then sign of determinant changes.

• If any two rows or any two columns are identical or proportional, then value of determinant is zero.

• If we multiply each element of a row or a column of a determinant by constant k, then value of determinant is multiplied by k.

• Multiplying a determinant by k means multiply elements of only one row (or one column) by k.

•If A= [ a_{ij} ]_{3×3} , then |k. A| =k^{3} | A |

• If elements of a row or a column in a determinant can be expressed as sum of two or more elements, then the given determinant can be expressed as sum of two or more determinants.

• If to each element of a row or a column of a determinant the equimultiples of corresponding elements of other rows or columns are added, then value of determinant remains same.

• Area of a triangle with vertices ( x_{1}, y_{1} ), ( x_{2}, y_{2} ) and ( x_{3}, y_{3} ) is given by

• Minor of an element aij of the determinant of matrix A is the determinant obtained by deleting th i row and th j column and denoted by Mij

• Cofactor of aij of given by Aij = (– 1)i+ j Mij

• Value of determinant of a matrix A is obtained by sum of product of elements of a row (or a column) with corresponding cofactors. For example, |A| = a_{11 }A_{11} + a_{12} A_{12} + a_{13} A_{13} .

• If elements of one row (or column) are multiplied with cofactors of elements of any other row (or column), then their sum is zero. For example

• If elements of one row (or column) are multiplied with cofactors of elements of any other row (or column), then their sum is zero. For example, a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} = 0

• A (adj A) = (adj A) A = | A | I ,where A is square matrix of order n.

• A square matrix A is said to be singular or non-singular according as |A|| = 0 or |A| ≠ 0.

• If AB = BA = I, where B is square matrix, then B is called inverse of A. Also A^{-1} = B or B-1 = A and human (A^{-1})^{-1} = A

• A square matrix A has inverse if and only if A is non-singular.

• If a_{1}x + b_{1}y + c_{1}z = d_{1}

• a_{2}x + b_{2}y + c_{2}z = d_{2}

• a_{3}x + b_{3}y + c_{3}z = d_{3}

• then these equations can be written as A X = B, where

• Unique solution of equation AX = B is given by X = A^{-1} B, where | A| 0 ≠ 0

• A system of equation is consistent or inconsistent according as its solution exists or not.

• For a square matrix A in matrix equation AX = B

• ||A| ≠ 0, there exists unique solution

• |A| = 0 and (adj A) B ≠ 0, then there exists no solution

• |A| = 0 and (adj A) B = 0, then system may or may not be consistent.

## Mathematics Determinants Worksheets for Class 12 as per CBSE NCERT pattern

Parents and students are welcome to download as many worksheets as they want as we have provided all free. As you can see we have covered all topics which are there in your Class 12 Mathematics Determinants book designed as per CBSE, NCERT and KVS syllabus and examination pattern. These test papers have been used in various schools and have helped students to practice and improve their grades in school and have also helped them to appear in other school level exams. You can take printout of these chapter wise test sheets having questions relating to each topic and practice them daily so that you can thoroughly understand each concept and get better marks. As Mathematics Determinants for Class 12 is a very scoring subject, if you download and do these questions and answers on daily basis, this will help you to become master in this subject.

**Benefits of Free Determinants Worksheet Class 12 Maths**

- You can improve understanding of your concepts if you solve NCERT Class 12 Mathematics Determinants Worksheets,
- These CBSE Class 12 Mathematics Determinants worksheets can help you to understand the pattern of questions expected in Mathematics Determinants exams.
- All worksheets for Mathematics Determinants Class 12 for NCERT have been organized in a manner to allow easy download in PDF format
- Parents will be easily able to understand the worksheets and give them to kids to solve
- Will help you to quickly revise all chapters of Class 12 Mathematics Determinants textbook
- CBSE Class 12 Mathematics Determinants Workbook will surely help to improve knowledge of this subject

These Printable practice worksheets are available for free download for Class 12 Mathematics Determinants. As the teachers have done extensive research for all topics and have then made these worksheets for you so that you can use them for your benefit and have also provided to you for each chapter in your ebook. The Chapter wise question bank and revision worksheets can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 12 Mathematics Determinants Worksheets PDF.

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