Comprehensive Study on Clinical Case Study Method

The clinical case study method involves an in-depth study focused on specific cases for detection, diagnosis, and treatment of behavioral issues. It includes steps like data collection, analysis, report writing, and offers merits and limitations. While effective in understanding individual and social groups, it can be subjective, costly, and time-consuming. This method is particularly useful in addressing problems in children and socially vulnerable groups.

• Clinical Case Study
• In-depth Study
• Behavioral Issues
• Data Analysis
• Treatment

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1. Chapter Chapter 4 4 Determinants Determinants This presentation includes the following topics Introduction Expansion of Introduction Expansion of determinants determinants

2. Determinants :- To every square matrix A = [aij] of order n, we can associate a number (real or complex ) called determinant of the square matrix A. Which is denoted by det A or |A|. This may be thought as a function which associates each square matrix with a unique real or complex number i.e f : M ---->K given by f(A) = det A = |A|, where M is the set of square matrices and K is the set of numbers (real or complex) If A = a b then det A = |A| = c d c d Sometimes determinant is also denoted by . Note : only square matrix can have determinant. a b

3. Determinant of a matrix of order two let A = a11 a12 a21 a22 Then the determinant of A is defined as : det A = |A| = = a11 be a matrix of order 2 x 2 . a12 a22 = a11 a22 - a21 a12 a21 Example 1: Evaluate 2 4 = 2(2) 4 (-1) = 4 + 4 = 8 -1 2 Determinant of a matrix of order 3 x 3 Consider the determinant of square matrix A = [aij]3 x 3 then a11 |A| = a21 a31 a12 a22 a32 a13 a23 = det A a33

4. Expansion along first Row ( R1 ):- To evaluate the determinant we can expand the determinant along any of the row or column. These are the steps to evaluate the given determinant by expending it along the first row (R1 ) : Step 1: Multiply first element a11 of R1 by (-1)(1+1) i.e (-1)(1+1) a11 a22 a23 = (-1)2 a11 ( a22.a33 a32.a23) a32 a33 Step 2: Multiply 2ndelement a12 of R1 by (-1)(1+2) i.e (-1)(1+2) a12 a21 a23 = (-1)3a12 (a21.a33 a31.a23) a31 a33 Step 3: Multiply 3rdelement a13of R1 by (-1)(1+3) i. (-1)(1+3) a13 a21 a22 = (-1)4a13 (a21.a32- a31.a22) a31 a32 Step 4 : Now the expansion of |A| is obtained by adding above three values and we get the requaired value of det A.