Chapter 3 Matrices and Determinants

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Math    Part-I    Chapter-III  "Matrices and Determinants

"Following are the key points that should be kept in mind while preparing this chapter in perspective of Entrance test of Universities.

• Understand the concept of Order of a Matrix and its relation with elements of a matrix.Order of a matrix is equal to number of members of a matrix.For example a matrix of order 3x4 will have 12 elements.So if number of elements are given , we can tell how many different order matrices can be formed using that number of elements. for example we can make '3' different order matrices using '9' elements as : 3x3 , 1x9 , 9x1. 

• Types , operations and Properties of matrices.

• Properties of Determinants.

• Echelon and Reduced Echelon Forms.

• Rank of a Matrix.

• Here is a shortcut for finding rank of a matrix but this method works mostly for rectangular matrices.Keep in mind that rank of a matrix cannot be negative and also cannot be greater than row number of a matrix.The method is that first add the elements of first row and write down the sum then the second row and write down the sum.Proceed until the rows are finished.Now add first column and write down the sum and do the same until columns end.Now you will have these sums(If order of matrix is 3x4 then sums will be 7).Cut negative numbers and the numbers greater than row number of under consideration matrix.All the remaining numbers will be possible of being ranks but the greatest of these will be the rank.

• Sum of the principal Diagonal Elements in a square matrix is called TRACE.

• If a matrix becomes ZERO when raised to higher Powers , It is called Nill-Potent Matrix.

• The Trace of a square Nill-Potent Matrix is always Zero.

• If a matrix becomes identity matrix when raised to higher powers then it is named as Idem-Potent Matrix.

• Study Page-130 of text book.