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Use augmented matrices to find the multiplicative inverse of the matri..
Use augmented matrices to find the multiplicative inverse of the matrix B = ( - 1 - 1 1 2 1 1 1 0 2 ) . => ( 1 0 0 0 1 0 0 0 1 ) or Does not exist or ( 1 1 - 1 - 2 - 1 - 1 - 1 0 - 2 ) or ( - 1 2 1 1 0 - 2 1 2 0 )..
Operations on Matrices
Equality of Matrices, Addition of Matrices, Matrix Addition is commutative, Matrix addition is associative, Subtraction of Matrices, Multiplication of a matrix by a scalar, Multiplication of Matrices, Properties of Matrix Multip..
Theorem:
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative..
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative..Linear Algebra
Types of linear systems Gauss-Jordan elimination, Gauss-Jordan method Vectors and vector addition Geometrical solution sets of systems of equations Rectangular matrices to row echelon form Matrix multiplication Inverse to a square matrix Determinants of 2 by 2..
Summary
A matrix is a rectangular array of numbers, arranged in rows and columns. Order of a matrix = Number of rows in it x Number of columns in it Row matrix is a matrix with only one row. Column matrix is a matrix with only one colum..
Summary
A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices ..
Matrices and Determinants Summary
Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matr..
Algebra/Linear Algebra
>Problems involving proportional change Factoring, exponents and variation Operations on rational expressions Quadratic equations Rate, work, percent, mixture problems Gauss-Jordan elimination Rectangular matrices to row echelon form Matrix/vector addition Matrix/vector mul..
Properties of Determinants
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..Polysaccharides
Polysaccharides are complex carbohydrates formed from monosaccharides. A number of monosaccharide molecules such as those of glucose, become linked by glycosidic bonds with the elimination of a molecule of water for each monosaccharide added. When a polysaccharide has multiple molecules o..
Polysaccharides are complex carbohydrates formed from monosaccharides. A number of monosaccharide molecules such as those of glucose, become linked by glycosidic bonds with the elimination of a molecule of water for each monosaccharide added. When a polysaccharide has multiple molecules o.. Result
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