In this post you will get Determinants Question Bank which is useful for B. Com 2nd Sem and 4th Sem CBCS Pattern and Class 12 ASHEC. In this question bank, all the questions asked in past exams are included. Questions are arranged according to type of questions asked in examination:
– Theoretical Questions
– Short answer type question (1 Mark)
– Prove That by using properties of determinants (3 to 5 Marks)
– Solve and find the value of X
– Solve the following by Cramer’s rule
– Multiplication of Two matrices
Determinants Question Bank [For BCOM Exam CBCS Pattern]
Introduction to Determinants
The theory of determinants had its origin in the study of system of linear equations but is has many other applications as well. Many complicated and lengthy expressions which require great strain for solutions can easily be solved if they are expressed as determinants.
Difference between Matrix and Determinant:
1. A matrix is a group of numbers, and a determinant is a unique number related to that matrix.
2. A determinant can be obtained from square matrices, but not the other way around. A determinant cannot give a unique matrix associated with it.
3. The algebra concerning the matrices and determinants has similarities and differences. Especially when performing multiplications. For example, multiplication of matrices has to be done element wise, where determinants are single numbers and follows simple multiplication.
4. Determinants are used to calculate the inverse of the matrix and if the determinant is zero the inverse of the matrix does not exist.
Properties of determinants
1. For a square matrix, the sum of the product of elements of any row (or column) with their cofactors is always equal to determinants of the matrix.
2. For a square matrix, the sum of the product of elements of any row (or column) with the cofactors of corresponding elements of some other row (or column) is zero.
3. The value of a determinant remains unchanged if its rows and columns are interchanged.
4. If any two rows (or columns) of a determinant are interchanged, then the value of the determinant changes by minus sign only.
5. If any two rows or columns of a determinant are identical then its value is zero.
6. If each element of a row (or a column) of a determinant is multiplied by a constant k, then the value of the new determinant is ‘k’ times the value of the original determinant.
7. If each element of a row (or column) in a determinant is zero, then its value is zero.
8. If the matrix is a diagonal square matrix then its determinant is the product of all the diagonal elements.
9. If A and B are square matrices of the same order, then |AB| = |A| |B|
12. If a matrix is a triangular matrix of order n, then its determinant is the product of all the diagonal elements.
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