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## Our Linear Algebra Tutorials: at a glanceLinear Algebra - Matrices Part I - A Tutorial with ExamplesLinear Algerba - Matrices Part II - Tutorial with Problems and SolutionsLinear Algebra - Determinants - A Tutorial with Problems and SolutionsLinear Algebra - Simultaneous Equations in Multiple Variables Basic Concepts In Linear Algebra and Vector Spaces - A Tutorial with Examples and Solved ProblemsLinear Algebra - Introductory Problems Related to Vector SpacesLinear Algebra - More about Vector SpacesLinear Algebra - Linear Transformations, Operators and MapsLinear Algebra - Eigenvalues, Eigenvector,Cayley Hamilton TheoremLinear Algebra - Problems on Simultaneous Equations, EigenvectorsLinear Algebra - A few closing problems in Recurrence Relations

Linear Algebra: Determinants

#### Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE, Anyone else who needs this Tutorial as a reference!

 Introduction to determinants. Second and third order determinants, minors and co-factors. Properties of determinants and how it remains altered or unaltered based on simple transformations is matrices. Expanding the determinant. Solved problems related to determinants.

#### Here's a quick outline of the topics covered in this tutorial

1. Determinants :
2. Computing the minors and co-factorsminor Mijthjth(i+j) ijij
3. Expansion of Determinant: A determinant can be evaluated by taking elements of any row

or column and multiplying with their cofactors; and adding the results.

#### Properties of Determinants :

1. If rows and columns are interchanged, the determinant remains unaltered.
2. If any 2 rows or columns of a determinant are interchanged, then the resulting
determinant is the negative of the original determinant
3. If the elements of any row (column) are multiplied by a non-zero scalar k, then the
determinant is multiplied by k.
4. If two rows(or columns) in a determinant have corresponding entries that are equal,
the value of determinant is equal to zero.
5. If each entry of a determinant is written as sum of two or more constituents then the determinant can be expressed as a sum of two or more determinants.
6. If to each element of a line (row or columns) of a determinant be added the equi-multiple of the corresponding elements of one or parallel lines, the determinant remains unaltered.
7. If each entry in any row or a column is zero then value of a determinant is zero.
We introduce the idea of solving simultaneous equations using determinants.
Consider a system of mn
1. Solution:
2. Consistent system:
3. Homogeneous and non-homogeneous system of linear equations:

Tutorial with solved problems :
These problems will help you understand how to apply row and column transformations to compute determinants. Computing and simplifying determinants involving terms with factorials, log, trigonometric ratios, algebraic expressions and so on.