 75.1: Find each product.
 75.2: Find each product.
 75.3: Find each product.
 75.4: Find each product.
 75.5: Simplify.
 75.6: Simplify.
 75.7: Simplify.
 75.8: Simplify.
 75.9: SAVINGS For Exercises 911, use the following information. Matthews ...
 75.10: SAVINGS For Exercises 911, use the following information. Matthews ...
 75.11: SAVINGS For Exercises 911, use the following information. Matthews ...
 75.12: Solve each equation.
 75.13: Solve each equation.
 75.14: Solve each equation.
 75.15: Solve each equation.
 75.16: Find each product.
 75.17: Find each product.
 75.18: Find each product.
 75.19: Find each product.
 75.20: Find each product.
 75.21: Find each product.
 75.22: Find each product.
 75.23: Find each product.
 75.24: Find each product.
 75.25: Find each product.
 75.26: Simplify.
 75.27: Simplify.
 75.28: Simplify.
 75.29: Simplify.
 75.30: Simplify.
 75.31: Simplify.
 75.32: SAVINGS For Exercises 32 and 33, use the following information. Mar...
 75.33: SAVINGS For Exercises 32 and 33, use the following information. Mar...
 75.34: FARMING A farmer plants corn in a field with a length to width rati...
 75.35: CLASS TRIP Mr. Wongs American History class will take taxis from th...
 75.36: Solve each equation.
 75.37: Solve each equation.
 75.38: Solve each equation.
 75.39: Solve each equation.
 75.40: Solve each equation.
 75.41: Solve each equation.
 75.42: Expand and simplify.
 75.43: Expand and simplify.
 75.44: Find each product.
 75.45: Find each product.
 75.46: Find each product.
 75.47: Find each product.
 75.48: Simplify.
 75.49: Simplify.
 75.50: Solve each equation.
 75.51: Solve each equation.
 75.52: GEOMETRY Find the area of each shaded region in simplest form.
 75.53: GEOMETRY Find the area of each shaded region in simplest form.
 75.54: VOLUNTEERING For Exercises 54 and 55, use the following information...
 75.55: VOLUNTEERING For Exercises 54 and 55, use the following information...
 75.56: SALES For Exercises 56 and 57, use the following information. A sto...
 75.57: SALES For Exercises 56 and 57, use the following information. A sto...
 75.58: SPORTS You may have noticed that when runners race around a curved ...
 75.59: NUMBER THEORY For Exercises 59 and 60, let x be an odd integer.
 75.60: NUMBER THEORY For Exercises 59 and 60, let x be an odd integer.
 75.61: OPEN ENDED Write a monomial and a trinomial involving one variable....
 75.62: CHALLENGE For Exercises 6264, use the following information. An eve...
 75.63: CHALLENGE For Exercises 6264, use the following information. An eve...
 75.64: CHALLENGE For Exercises 6264, use the following information. An eve...
 75.65: Writing in Math Use the information about the area of a rectangle o...
 75.66: A plumber charges $70 for the first thirty minutes of each house ca...
 75.67: REVIEW What is the slope of this line? F _5 2 G 2 H _1 2 J _2 5
 75.68: Find each sum or difference.
 75.69: Find each sum or difference.
 75.70: Find each sum or difference.
 75.71: Find each sum or difference.
 75.72: State whether each expression is a polynomial. If the expression is...
 75.73: State whether each expression is a polynomial. If the expression is...
 75.74: State whether each expression is a polynomial. If the expression is...
 75.75: State whether each expression is a polynomial. If the expression is...
 75.76: Define a variable, write an inequality, and solve each problem. The...
 75.77: Define a variable, write an inequality, and solve each problem. The...
 75.78: Write an equation of the line that passes through each pair of points.
 75.79: Write an equation of the line that passes through each pair of points.
 75.80: Write an equation of the line that passes through each pair of points.
 75.81: Solve each equation.
 75.82: Solve each equation.
 75.83: Solve each equation.
 75.84: BASKETBALL Tremaine scored 54 threepoint field goals, 84 twopoint...
 75.85: PREREQUISITE SKILL Simplify
 75.86: PREREQUISITE SKILL Simplify
 75.87: PREREQUISITE SKILL Simplify
 75.88: PREREQUISITE SKILL Simplify
 75.89: PREREQUISITE SKILL Simplify
 75.90: PREREQUISITE SKILL Simplify
Solutions for Chapter 75: Multiplying a Polynomial by a Monomial
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 75: Multiplying a Polynomial by a Monomial
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 90 problems in chapter 75: Multiplying a Polynomial by a Monomial have been answered, more than 23048 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 75: Multiplying a Polynomial by a Monomial includes 90 full stepbystep solutions. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = 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).

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.