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Solutions for Chapter 10-6: Similar Triangles

Algebra 1, Student Edition (MERRILL ALGEBRA 1) | 1st Edition | ISBN: 9780078738227 | Authors: Berchie Holliday, Gilbert J. Cuevas, Beatrice Luchin, Ruth M. Casey, Linda M. Hayek, John A. Carter, Daniel Marks, Roger Day, & 2 more

Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1) | 1st Edition

ISBN: 9780078738227

Algebra 1, Student Edition (MERRILL ALGEBRA 1) | 1st Edition | ISBN: 9780078738227 | Authors: Berchie Holliday, Gilbert J. Cuevas, Beatrice Luchin, Ruth M. Casey, Linda M. Hayek, John A. Carter, Daniel Marks, Roger Day, & 2 more

Solutions for Chapter 10-6: Similar Triangles

Solutions for Chapter 10-6
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Textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1)
Edition: 1
Author: Berchie Holliday, Gilbert J. Cuevas, Beatrice Luchin, Ruth M. Casey, Linda M. Hayek, John A. Carter, Daniel Marks, Roger Day, & 2 more
ISBN: 9780078738227

This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 46 problems in chapter 10-6: Similar Triangles have been answered, more than 35424 students have viewed full step-by-step solutions from this chapter. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Chapter 10-6: Similar Triangles includes 46 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Math Terms and definitions covered in this textbook
  • Cholesky factorization

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

  • Condition number

    cond(A) = c(A) = IIAIlIIA-III = 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.

  • Cross product u xv in R3:

    Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

  • Eigenvalue A and eigenvector x.

    Ax = AX with x#-O so det(A - AI) = o.

  • 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 Fn-1c can be computed with ne/2 multiplications. Revolutionary.

  • Fundamental Theorem.

    The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n - r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

  • Hermitian matrix A H = AT = A.

    Complex analog a j i = aU of a symmetric matrix.

  • Hypercube matrix pl.

    Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

  • Identity matrix I (or In).

    Diagonal entries = 1, off-diagonal entries = 0.

  • lA-II = l/lAI and IATI = IAI.

    The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n - 1, volume of box = I det( A) I.

  • 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.

  • Matrix multiplication AB.

    The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

  • 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).

  • Nilpotent matrix N.

    Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

  • Nullspace matrix N.

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

  • Projection p = a(aTblaTa) onto the line through a.

    P = aaT laTa has rank l.

  • Row space C (AT) = all combinations of rows of A.

    Column vectors by convention.

  • Semidefinite matrix A.

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

  • Simplex method for linear programming.

    The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

  • Subspace S of V.

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

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