 6.7.1: What is the interest due if $500 is borrowed for 6 months at a simp...
 6.7.2: If you borrow $5000 and, after 9 months, pay off the loan in the am...
 6.7.3: The total amount borrowed (whether by an individual from a bank in ...
 6.7.4: If a principal of P dollars is borrowed for a period of t years at ...
 6.7.5: In working problems involving interest, if the payment period of th...
 6.7.6: The is the equivalent annual simple interest rate that would yield ...
 6.7.7: In 714, find the amount that results from each investment.$100 inve...
 6.7.8: In 714, find the amount that results from each investment.$50 inves...
 6.7.9: In 714, find the amount that results from each investment.$500 inve...
 6.7.10: In 714, find the amount that results from each investment.$300 inve...
 6.7.11: In 714, find the amount that results from each investment.$600 inve...
 6.7.12: In 714, find the amount that results from each investment.$700 inve...
 6.7.13: In 714, find the amount that results from each investment.$1000 inv...
 6.7.14: In 714, find the amount that results from each investment.$400 inve...
 6.7.15: In 1522, find the principal needed now to get each amount; that is,...
 6.7.16: In 1522, find the principal needed now to get each amount; that is,...
 6.7.17: In 1522, find the principal needed now to get each amount; that is,...
 6.7.18: In 1522, find the principal needed now to get each amount; that is,...
 6.7.19: In 1522, find the principal needed now to get each amount; that is,...
 6.7.20: In 1522, find the principal needed now to get each amount; that is,...
 6.7.21: In 1522, find the principal needed now to get each amount; that is,...
 6.7.22: In 1522, find the principal needed now to get each amount; that is,...
 6.7.23: In 2326, find the effective rate of interest. For 5% compounded qua...
 6.7.24: In 2326, find the effective rate of interest. For 6% compounded mon...
 6.7.25: In 2326, find the effective rate of interest. For 5% compounded con...
 6.7.26: In 2326, find the effective rate of interest. For 6% compounded con...
 6.7.27: In 2730, determine the rate that represents the better deal. 6% com...
 6.7.28: In 2730, determine the rate that represents the better deal. 9% com...
 6.7.29: In 2730, determine the rate that represents the better deal. 9% com...
 6.7.30: In 2730, determine the rate that represents the better deal. 8% com...
 6.7.31: What rate of interest compounded annually is required todouble an i...
 6.7.32: What rate of interest compounded annually is required todouble an i...
 6.7.33: What rate of interest compounded annually is required totriple an i...
 6.7.34: What rate of interest compounded annually is required totriple an i...
 6.7.35: (a) How long does it take for an investment to double in value if i...
 6.7.36: (a) How long does it take for an investment to triple in value if i...
 6.7.37: What rate of interest compounded quarterly will yield an effective ...
 6.7.38: What rate of interest compounded continuously will yield an effecti...
 6.7.39: Time Required to Reach a Goal If Tanisha has $100 to invest at 8% p...
 6.7.40: Time Required to Reach a Goal If Angela has $100 to invest at 10% p...
 6.7.41: Time Required to Reach a Goal How many years will it take for an in...
 6.7.42: Time Required to Reach a Goal How many years will it take for an in...
 6.7.43: Price Appreciation of Homes What will a $90,000 condominium cost 5 ...
 6.7.44: Credit Card Interest A department store charges 1.25% per month on ...
 6.7.45: Saving for a Car Jerome will be buying a used car for $15,000 in 3 ...
 6.7.46: Paying off a Loan John requires $3000 in 6 months to pay off a loan...
 6.7.47: Return on a Stock George contemplates the purchase of 100 shares of...
 6.7.48: Return on an Investment A business purchased for $650,000 in 2005 i...
 6.7.49: Comparing Savings Plans Jim places $1000 in a bank account that pay...
 6.7.50: Savings Plans On January 1, Kim places $1000 in a certificate of de...
 6.7.51: Comparing IRA Investments Will invests $2000 in his IRA in a bond t...
 6.7.52: Comparing Two Alternatives Suppose that April has access to an inve...
 6.7.53: College Costs The average annual cost of college at 4year private ...
 6.7.54: Analyzing Interest Rates on a Mortgage Colleen and Bill have just p...
 6.7.55: 2009 Federal Stimulus Package In February 2009, President Obama sig...
 6.7.56: Per Capita Federal Debt In 2008, the federal debt was about $10 tri...
 6.7.57: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.58: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.59: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.60: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.61: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.62: Inflation 5762 require the following discussion. Inflation is a ter...
 6.7.63: 6366 involve zerocoupon bonds.A zerocoupon bond is a bond that is...
 6.7.64: 6366 involve zerocoupon bonds.A zerocoupon bond is a bond that is...
 6.7.65: 6366 involve zerocoupon bonds.A zerocoupon bond is a bond that is...
 6.7.66: 6366 involve zerocoupon bonds.A zerocoupon bond is a bond that is...
 6.7.67: Time to Double or Triple an Investment The formula can be used to f...
 6.7.68: Time to Reach an Investment Goal The formula can be used to find th...
 6.7.69: 6972 require the following discussion.The Consumer Price Index (CPI...
 6.7.70: 6972 require the following discussion.The Consumer Price Index (CPI...
 6.7.71: 6972 require the following discussion.The Consumer Price Index (CPI...
 6.7.72: 6972 require the following discussion.The Consumer Price Index (CPI...
 6.7.73: Explain in your own words what the term compound interest means.Wha...
 6.7.74: Explain in your own words the meaning of present value.
 6.7.75: Critical Thinking You have just contracted to buy a house and will ...
Solutions for Chapter 6.7: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 6.7
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 6.7 includes 75 full stepbystep solutions. Since 75 problems in chapter 6.7 have been answered, more than 55859 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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).

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

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

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.