 4.2.4.1.85: Another name for a placevalue system is a(n) value system.
 4.2.4.1.86: In the numeral 234, the 2 represents 2 .
 4.2.4.1.87: In the numeral 234, the 3 represents 3
 4.2.4.1.88: In the numeral 234, the 4 represents 4 .
 4.2.4.1.89: The most common positional system is the decimal number system whic...
 4.2.4.1.90: The base 10 system was developed from counting on .
 4.2.4.1.91: When we write 789 as (7 * 102 ) + (8 * 10) + (9 * 1) the number is ...
 4.2.4.1.92: The Babylonian system is not considered a true placevalue system b...
 4.2.4.1.93: The base used in the Babylonian system is .
 4.2.4.1.94: In the Babylonian numeration system, a) the symbol represents the n...
 4.2.4.1.95: t is believed that the Mayans used 18 20 instead of 202 so that the...
 4.2.4.1.96: In the Mayan numeration system, a) the symbol represents the numera...
 4.2.4.1.97: In Exercises 1324, write the HinduArabic numeral in expanded form. 58
 4.2.4.1.98: In Exercises 1324, write the HinduArabic numeral in expanded form. 93
 4.2.4.1.99: In Exercises 1324, write the HinduArabic numeral in expanded form.712
 4.2.4.1.100: In Exercises 1324, write the HinduArabic numeral in expanded form.562
 4.2.4.1.101: In Exercises 1324, write the HinduArabic numeral in expanded form. 897
 4.2.4.1.102: In Exercises 1324, write the HinduArabic numeral in expanded form.3769
 4.2.4.1.103: In Exercises 1324, write the HinduArabic numeral in expanded form. ...
 4.2.4.1.104: In Exercises 1324, write the HinduArabic numeral in expanded form. ...
 4.2.4.1.105: In Exercises 1324, write the HinduArabic numeral in expanded form.1...
 4.2.4.1.106: In Exercises 1324, write the HinduArabic numeral in expanded form.1...
 4.2.4.1.107: In Exercises 1324, write the HinduArabic numeral in expanded form.3...
 4.2.4.1.108: In Exercises 1324, write the HinduArabic numeral in expanded form.3...
 4.2.4.1.109: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.110: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.111: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.112: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.113: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.114: In Exercises 2530, write the Babylonian numeral as a HinduArabic nu...
 4.2.4.1.115: In Exercises 3136, write the numeral as a Babylonian numeral.41
 4.2.4.1.116: In Exercises 3136, write the numeral as a Babylonian numeral.129
 4.2.4.1.117: In Exercises 3136, write the numeral as a Babylonian numeral.471
 4.2.4.1.118: In Exercises 3136, write the numeral as a Babylonian numeral.512
 4.2.4.1.119: In Exercises 3136, write the numeral as a Babylonian numeral.3605
 4.2.4.1.120: In Exercises 3136, write the numeral as a Babylonian numeral.12,435
 4.2.4.1.121: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.122: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.123: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.124: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.125: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.126: In Exercises 3742, write the Mayan numeral as a Hindu Arabic numeral.
 4.2.4.1.127: In Exercises 4348, write the numeral as a Mayan numeral.18
 4.2.4.1.128: In Exercises 4348, write the numeral as a Mayan numeral. 257
 4.2.4.1.129: In Exercises 4348, write the numeral as a Mayan numeral.297
 4.2.4.1.130: In Exercises 4348, write the numeral as a Mayan numeral.406
 4.2.4.1.131: In Exercises 4348, write the numeral as a Mayan numeral.2163
 4.2.4.1.132: In Exercises 4348, write the numeral as a Mayan numeral.17,708
 4.2.4.1.133: In Exercises 49 and 50, write the numeral in the indicated systems ...
 4.2.4.1.134: In Exercises 49 and 50, write the numeral in the indicated systems ...
 4.2.4.1.135: In Exercises 51 and 52, suppose a placevalue numeration system has...
 4.2.4.1.136: In Exercises 51 and 52, suppose a placevalue numeration system has...
 4.2.4.1.137: Describe two ways that the Mayan placevalue system differs from th...
 4.2.4.1.138: a) The Babylonian system did not have a symbol for zero. Why did th...
 4.2.4.1.139: a) Write the Mayan numeral for 999,999. b) Write the Babylonian num...
 4.2.4.1.140: In Exercises 5659, first convert each numeral to a Hindu Arabic num...
 4.2.4.1.141: In Exercises 5659, first convert each numeral to a Hindu Arabic num...
 4.2.4.1.142: In Exercises 5659, first convert each numeral to a Hindu Arabic num...
 4.2.4.1.143: In Exercises 5659, first convert each numeral to a Hindu Arabic num...
 4.2.4.1.144: Your Own System Create your own placevalue system. Write 2013 in y...
 4.2.4.1.145: Investigate and write a report on the development of the HinduArabi...
 4.2.4.1.146: The Arabic numeration system currently in use is a base 10 position...
Solutions for Chapter 4.2: Systems of Numeration
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 4.2: Systems of Numeration
Get Full SolutionsThis textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. Chapter 4.2: Systems of Numeration includes 62 full stepbystep solutions. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. Since 62 problems in chapter 4.2: Systems of Numeration have been answered, more than 79863 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Solvable system Ax = b.
The right side b is in the column space of A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.