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Singular Matrix, Non-singular Matrix, [2 1, D=| 1, 1 1, 1, 1, C=| 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 11, 1, 12, 1, 11, ICI = 1, 1, 1, IDI = 1, 2, 1, I 1, 1, 11, 1 1, 1, 11, ICI =, IDI =, 2, 2, 1, 2 x |, 1, 1x, +1x, -1x, 1, 1, 1, =1x(1x1-1x1)-1x(1x1-1x1)+1x(1x1-, =2x(2x1-1x1)-1x(1x1-1x1)+1x(1x1-2x1), 1x1), =2x(2-1)-1x(1-1)+1x(1-2), =1x(1-1)-1x(1-1)+1x(1-1), =2x(1)-1x(0)+1x(-1), =1x(0)-1x(0)+1x(0), =2-0-1, =0+0+0, =1, Here, ICI = o, so Cis a singular, Here, IDI +O, so D is a non-singular, matrix, matrix, Row and Column Matrix, Matrices with only one row and any number of columns are known as row, matrices and matrices with one column and any number of rows are, called column matrices. Let's look at two examples below:, Row Matrix, Column Matrix, A = [1 0 2 4], B =, There is only one column, so B is, a column matrix., There is only one row, so A is a, row matrix., 325

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Rectangular and Square Matrix, Any matrix that does not have an equal number of rows and columns is, called a rectangular matrix and a rectangular matrix can be denoted by, [B]mxn. Any matrix that has an equal number of rows and columns is, called a square matrix and a square matrix can be denoted by [B]nxn-, Let's look at the examples below:, Rectangular Matrix, Square Matrix, -1, -1, 3, B =, 2, C =, 1, -1, -2, 1, -1, -2, There are three rows and four, There are three rows and three, columns in this matrix, so C is a, columns in this matrix, so B is a, rectangular matrix., square matrix., Algebra of Matrix, Algebra of matrix involves the operation of matrices, such as Addition, subtraction, multiplication etc., Let us understand the operation of the matrix in a much better way-, Addition/Subtraction of Matrices, Two matrices can be added/subtracted, iff (if and only if) the number of rows and columns of both the matrices, are same, or the order of the matrices are equal., For addition/subtraction, each element of the first matrix is added/subtracted to the elements present in the 2nd, matrix., An Ap A, Bu Bu, Ba, An Az . A, Bai Ba, Ba, Aa: Ana ., Aan, Bal Baz, * Ban, An +B1, A12+ B2, An+ B, An+ Bai An +B22, A+ Ba, Anl+ Bai Aa +Baa .., Aan + Ban, Example:, 2 0 5, 3 2 9, 7., 4, 1, 9., 4, 13 0, 11, 15 9, LO - O, 2.