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
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,
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