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# Introduction of Determinant

#### notes

To every square matrix A = [a_(ij)] of order n, we can associate a number (real or complex) called determinant of the square matrix A, where a_(ij) = (i, j)^(th) element of A. This may be thought of as a function which associates each square matrix with a unique number (real or complex). If M is the set of square matrices, K is the set of numbers (real or complex) and f : M → K is defined by f(A) = k, where A ∈ M and k ∈ K, then f(A) is called the determinant of A. It is also denoted by |A| or det A or ∆.
If A = [(a,b),(c,d)] , then determinants of A is written as |A| is written as |A| = |(a,b),(c,d)| = det (A)
Remarks:
(i) For matrix A, |A| is read as determinant of A and not modulus of A.
(ii) Only square matrices have determinants.

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Determinant Part 1 [00:25:38]
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