 10.5.1: The method of using determinants to solve a system of linear equati...
 10.5.2: Three points are ________ if the points lie on the same line.
 10.5.3: The area of a triangle with vertices and is given by ________.
 10.5.4: A message written according to a secret code is called a ________.
 10.5.5: To encode a message, choose an invertible matrix and multiply the _...
 10.5.6: If a message is encoded using an invertible matrix then the message...
 10.5.7:
 10.5.8: 4x
 10.5.9: 3x 2y 6x 4y 2 4
 10.5.10: 6x 5y 13x 3y 17 76
 10.5.11: 0.4x 0.8y 1.6 0.2x 0.3y 2.2
 10.5.12: 2.4x 1.3y 4.6x 0.5y 14.63 11.51 0
 10.5.13: 4x y z 2x 2y 3z 5x 2y 6z 5 10 1
 10.5.14: 4x 2y 3z 2x 2y 5z 8x 5y 2z 2 16 4 4
 10.5.15: x 2y 3z 2x y z 3x 3y 2z 3 6 11 4x
 10.5.16: 5x 4y z x 2y 2z 3x y z 14 10 1 x
 10.5.17: 3x 3y 5z 1 3x 5y 9z 2 5x 9y 17z 4
 10.5.18: x 2y z 2x 2y 2z x 3y 4z 7 8 8 3x
 10.5.19: 2x x 3x y 2y y z z z 5 1 4
 10.5.20: 3x 2x x y y y 3z 2z z 1 4 5 2
 10.5.21: ) (1, 5) (3, 1) 5 1 2 3 4 5 y
 10.5.22: (5, 2) (0, 0) 1 4 2 1 2 3 4 5 y
 10.5.23: (2, 3) (2, 3) 4 2 2 4 y
 10.5.24: y x (3, 1) 2
 10.5.25: 1 2 3 4 1 2 0, ( ) 5 2 , 0 x y
 10.5.26: (6, 1) (6, 10) (4, 5) 8 4 8 y
 10.5.27: 2, 4, 2, 3, 1, 5 0,
 10.5.28: 0, 2, 1, 4, 3, 5 (6
 10.5.29: 3, 5, 2, 6, 3, 5 2,
 10.5.30: 2, 4, 1, 5, 3, 2
 10.5.31: 4, 2, 0, 7 2, 3, 1 2
 10.5.32: 9 2, 0, 2, 6, 0, 3 2
 10.5.33: 5, 1, 0, 2, 2, y 4,
 10.5.34: 4, 2, 3, 5, 1, y y
 10.5.35: 2, 3, 1, 1, 8, y y
 10.5.36: 1, 0, 5, 3, 3, y
 10.5.37: AREA OF A REGION A large region of forest has been infested with gy...
 10.5.38: AREA OF A REGION You own a triangular tract of land, as shown in th...
 10.5.39: 3, 1, 0, 3, 12, 5 3
 10.5.40: 3, 5, 6, 1, 4, 2
 10.5.41: 2, 1 2, 4, 4, 6, 3 3,
 10.5.42: 0, 1 2, 2, 1, 4, 7 2 2
 10.5.43: 0, 2, 1, 2.4, 1, 1.6
 10.5.44: 2, 3, 3, 3.5, 1, 2
 10.5.45: 2, 5, 4, y, 5, 2 6
 10.5.46: 6, 2, 5, y, 3, 5 y
 10.5.47: 0, 0, 5, 3
 10.5.48: 0, 0, 2, 2
 10.5.49: 4, 3, 2, 1 1
 10.5.50: 10, 7, 2, 7 0
 10.5.51: , 4, 6, 12 1 2, 3, 5 2, 1
 10.5.52: 2 3 , 4, 6, 12
 10.5.53: COME HOME SOON
 10.5.54: HELP IS ON THE WAY
 10.5.55: CALL ME TOMORROW
 10.5.56: PLEASE SEND MONEY
 10.5.57: LANDING SUCCESSFUL
 10.5.58: ICEBERG DEAD AHEAD
 10.5.59: HAPPY BIRTHDAY
 10.5.60: OPERATION OVERLOAD
 10.5.61: A 1 3 2 5
 10.5.62: A 2 3 3 4
 10.5.63: A 1 1 6 1 0 2 0 1 3
 10.5.64: A 3 0 4 4 2 5 2 1 3 S
 10.5.65: 20 17 1 62 143 181
 10.5.66: 13 61 112 106 11 24 29 65 144 172
 10.5.67: The following cryptogram was encoded with a matrix. 8 21 5 10 5 25 ...
 10.5.68: The following cryptogram was encoded with a matrix. 5 2 25 11 32 14...
 10.5.69: DATA ANALYSIS: BOTTLED WATER The table shows the per capita consump...
 10.5.70: HAIR PRODUCTS A hair product company sells three types of hair prod...
 10.5.71: In Cramers Rule, the numerator is the determinant of the coefficien...
 10.5.72: You cannot use Cramers Rule when solving a system of linear equatio...
 10.5.73: In a system of linear equations, if the determinant of the coeffici...
 10.5.74: The points and are collinear.
 10.5.75: WRITING Use your schools library, the Internet, or some other refer...
 10.5.76: CAPSTONE
 10.5.77: Use determinants to find the area of a triangle with vertices and C...
Solutions for Chapter 10.5: Applications of Matrices and Determinants
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 10.5: Applications of Matrices and Determinants
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. Since 77 problems in chapter 10.5: Applications of Matrices and Determinants have been answered, more than 47623 students have viewed full stepbystep solutions from this chapter. Chapter 10.5: Applications of Matrices and Determinants includes 77 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.

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

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

Column space C (A) =
space of all combinations of the columns of A.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Iterative method.
A sequence of steps intended to approach the desired solution.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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.

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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.

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).