The Chemistry Maths Book, Second Edition

490 Chapter 17Determinants This follows from the expansion of the three determinants along the relevant row or column; column 1 ...

17.5 Properties of determinants 491 For interchange of rows EXAMPLE 17.12Determinant of order 3. By Example 17.2, Interchange of ...

492 Chapter 17Determinants Proportional rows or columns The value of a determinant is zeroif one row (or column) is a multiple ...

17.6 Reduction to triangular form 493 Linearly-dependent rows or columns The value of a determinant is zeroif the rows (or col ...

494 Chapter 17Determinants (17.51) Every determinant can be reduced to triangular form by means of a systematic application of P ...

17.7 Alternating functions 495 If two variables are equal the function is zero, f(x 1 , x 1 , x 3 , =, x n ) 1 = 10 (17.53) A de ...

496 Chapter 17Determinants *The wave function of a system of bosons is totally symmetric, and the interchange of the coordinates ...

17.8 Exercises 497 Section 17.3 Evaluate: Section 17.4 Use Cramer’s rule to solve the systems of equations: 3 x 1 ...

498 Chapter 17Determinants Section 17.6 Evaluate the following determinants by reduction to triangular form: Section ...

18 Matrices and linear transformations 18.1 Concepts Matrix algebra is the branch of mathematics concerned with the theory of sy ...

500 Chapter 18Matrices and linear transformations In this notation, the elementa ij lies in the ith row and jth column. Although ...

18.1 Concepts 501 EXAMPLE 18.1Rotation as a coordinate transformation Consider a point P in the xy-plane, with coordinates(x, y) ...

502 Chapter 18Matrices and linear transformations 18.2 Some special matrices Square matrices If the number of rows of a matrix i ...

18.2 Some special matrices 503 and the sum of the diagonal elements of the matrix, called the trace(or sometimes spur) of the ma ...

504 Chapter 18Matrices and linear transformations The transpose matrix The transposeA T (or¡) of anm 1 × 1 nmatrix Ais then 1 × ...

18.3 Matrix algebra 505 18.3 Matrix algebra Equality of matrices Two matrices,A 1 = 1 (a ij )andB 1 = 1 (b ij ), are equal if th ...

506 Chapter 18Matrices and linear transformations EXAMPLES 18.6Multiplication by a scalar If then 0 Exercise 19 It follows from ...

18.3 Matrix algebra 507 Matrix multiplication The matrix productC 1 = 1 AB(in this order, with Ato the left of B) is defined onl ...

508 Chapter 18Matrices and linear transformations EXAMPLES 18.8Matrix multiplication (i) Two square matrices: (ii) Two rectangul ...

18.3 Matrix algebra 509 Properties of matrix multiplication The associative law A(BC) 1 = 1 (AB)C 1 = 1 ABC (18.29) Matrix multi ...