M (carrying capacity), 475, 482

Main diagonal, of a matrix, 590

Maisey, John, 249

Major axis, of an ellipse, 676

Marginal cost, 227

Mastlin, Michael, 332

Mathematical induction, 752–758

Mathematical modeling. See also Modeling

• defined, 92

Matrix(ces), 589–620

• adding, 607–608, 609

• augmented, 590–592

• column, 590

• defined, 589–590

• determinants of. See Determinants

• equality of, 606–607

• Gaussian elimination and, 595–597

• Gauss-Jordan elimination and, 597–600

• identity, 614

• inverses of. See Matrix inverses

• multiplying, 610–614

• order of, 590

• row, 590

• in row-echelon and reduced row-echelon form, 594–595

• row equivalent, 592

• row operations and, 592–595

• scalar multiplication of, 608

• solving linear systems using, 590–595

• square, 590

• subtracting, 608–609

• systems of linear equations compared with, 593–594

Matrix equations, 609

Matrix inverses, 621–635

• applications involving, 628–629

• finding, 623–626

• multiplicative, 621–622

• solving systems of linear equations using, 627–628

• verifying, 622

Maurolico, Francesco, 754

Maximum area, finding, 325

Maximum value

• for a parabola, 319, 322

• relative, of a function, 237–239

McDonald’s coffee, 456

“Megatooth” shark, 249, 250–251

Members of sets, 3

Mercalli, Giuseppe, 490

Midpoint formula, 180–181

Minimum value

• for a parabola, 319, 322

• relative, of a function, 237–239

Minor(s), in a matrix, 637–638

Minor access, of an ellipse, 676

Mixture problems, modeling, 99

Modeling, 498–500

• of body weight versus metabolic rate for small animals, 499–500

• financial, 94–95

• geometric, 93–94

• Leontief input-output model and, 589, 599–600, 628–629

• with logarithmic functions, 468

• logarithmic growth model and, 499

• logistic growth model and, 475, 482

• of mixture problems, 99

• power growth model and, 500

• problem-solving procedure for, 92–93

• temperature inside a parked car, 498–499

• of uniform motion, 95–97

• using linear regression, 207–209

• Verhulst model and, 475, 482

• of work rate, 97–98

Monomials, 30–31, 37

• factoring out, 41–42

• multiplying with a trinomial, 33

Moving objects, tracking, 324–325

Multiplication. See also Product(s)

• of complex numbers, 122–123

• of fractions, 14

• of matrices, 610–614

• of polynomials, 33–38

• of radicals with different indexes, 66–67

• of rational expressions, 52–53

Multiplicative inverse of a matrix, 621–622

Multiplier effect, 738, 747

Music, harmony in, 496

Musical pitch, 495–496

• logarithmic scales of, 495–496

Music programs, counting, 768

Mutually exclusive events, probability of, 782–783