determinants notes class 12th

 determinants class 12 revision 

• The difference between matrix and determinant are 1. matrix has no value and can be in any order but 2. for determinant it has the value a fixed value and has only square order only.
• the most important question came in boards which are done wrong by many of the candidates that are..Q. evaluate the determinant by two methods ??  in this ques, we will have two methods of expansions:- 1.EXPANSION method 2. SAURUS method. 
• minor of the determinant which is defined as a cofactor of matrix and remembers we don't have to change the signs here.
• properties of determinants:- 1. if any two rows or columns of a determinant are identical, then the value of that determinant is always 0.'
• 2. any two rows of the determinant can change consecutively like 1 or2, 2or 3 no change in 1 and 3 ...,  if any two consecutive rows are interchanged of determinant, then the value of the determinant is multiplied by -1.
• 3. if any particular row or column of the determinant is expressed as the sum of two no. , then we can split them or that determinant into two parts of the same order that will not change again into its additive form.
• 4. in determinant, we can add and subtract divide and multiply each and every row or columns and even between three of them.
•  5. we can take commonly from determinant any no. as taking common, we will multiply and divide simultaneously.
• 6. if the row or column is o, then the matrix would be considered as 0.
• now they're a lot of questions that u can practice here as well we have arihant past papers for practice and a lot of rd solutions and it's extra questions.
• do practice 

thanks everybody for reading 📖