 8.1: In Exercises 14, determine the order of the matrix
 8.2: In Exercises 14, determine the order of the matrix
 8.3: In Exercises 14, determine the order of the matrix
 8.4: In Exercises 14, determine the order of the matrix
 8.5: In Exercises 5 and 6, write the augmented matrix for the system of ...
 8.6: In Exercises 5 and 6, write the augmented matrix for the system of ...
 8.7: In Exercises 7 and 8, write the system of linear equations represen...
 8.8: In Exercises 7 and 8, write the system of linear equations represen...
 8.9: In Exercises 9 and 10, write the matrix in rowechelon form. Rememb...
 8.10: In Exercises 9 and 10, write the matrix in rowechelon form. Rememb...
 8.11: In Exercises 1114, write the system of linear equations represented...
 8.12: In Exercises 1114, write the system of linear equations represented...
 8.13: In Exercises 1114, write the system of linear equations represented...
 8.14: In Exercises 1114, write the system of linear equations represented...
 8.15: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.16: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.17: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.18: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.19: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.20: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.21: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.22: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.23: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.24: In Exercises 1524, use matrices and Gaussian elimination with back...
 8.25: In Exercises 2528, use matrices and GaussJordan elimination to sol...
 8.26: In Exercises 2528, use matrices and GaussJordan elimination to sol...
 8.27: In Exercises 2528, use matrices and GaussJordan elimination to sol...
 8.28: In Exercises 2528, use matrices and GaussJordan elimination to sol...
 8.29: In Exercises 29 and 30, use the matrix capabilities of a graphing u...
 8.30: In Exercises 29 and 30, use the matrix capabilities of a graphing u...
 8.31: In Exercises 3134, find x and y
 8.32: In Exercises 3134, find x and y
 8.33: In Exercises 3134, find x and y
 8.34: In Exercises 3134, find x and y
 8.35: In Exercises 3538, if possible, find (a) (b) (c) and
 8.36: In Exercises 3538, if possible, find (a) (b) (c) and
 8.37: In Exercises 3538, if possible, find (a) (b) (c) and
 8.38: In Exercises 3538, if possible, find (a) (b) (c) and
 8.39: In Exercises 3942, perform the matrix operations. If it is not poss...
 8.40: In Exercises 3942, perform the matrix operations. If it is not poss...
 8.41: In Exercises 3942, perform the matrix operations. If it is not poss...
 8.42: In Exercises 3942, perform the matrix operations. If it is not poss...
 8.43: In Exercises 43 and 44, use the matrix capabilities of a graphing u...
 8.44: In Exercises 43 and 44, use the matrix capabilities of a graphing u...
 8.45: In Exercises 4548, solve for in the equation given
 8.46: In Exercises 4548, solve for in the equation given
 8.47: In Exercises 4548, solve for in the equation given
 8.48: In Exercises 4548, solve for in the equation given
 8.49: In Exercises 4952, find if possible.
 8.50: In Exercises 4952, find if possible.
 8.51: In Exercises 4952, find if possible.
 8.52: In Exercises 4952, find if possible.
 8.53: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.54: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.55: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.56: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.57: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.58: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.59: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.60: In Exercises 5360, perform the matrix operations. If it is not poss...
 8.61: In Exercises 61 and 62, use the matrix capabilities of a graphing u...
 8.62: In Exercises 61 and 62, use the matrix capabilities of a graphing u...
 8.63: Manufacturing A tire corporation has three factories, each of which...
 8.64: Manufacturing A corporation has four factories, each of which manuf...
 8.65: Manufacturing A manufacturing company produces three kinds of compu...
 8.66: LongDistance Plans The charges (in dollars per minute) of two long...
 8.67: In Exercises 6770, show that is the inverse of A
 8.68: In Exercises 6770, show that is the inverse of A
 8.69: In Exercises 6770, show that is the inverse of A
 8.70: In Exercises 6770, show that is the inverse of A
 8.71: In Exercises 7174, find the inverse of the matrix (if it exists).
 8.72: In Exercises 7174, find the inverse of the matrix (if it exists).
 8.73: In Exercises 7174, find the inverse of the matrix (if it exists).
 8.74: In Exercises 7174, find the inverse of the matrix (if it exists).
 8.75: In Exercises 7578,use the matrix capabilities of a graphing utility...
 8.76: In Exercises 7578,use the matrix capabilities of a graphing utility...
 8.77: In Exercises 7578,use the matrix capabilities of a graphing utility...
 8.78: In Exercises 7578,use the matrix capabilities of a graphing utility...
 8.79: In Exercises 7982, use the formula below to find the inverse of the...
 8.80: In Exercises 7982, use the formula below to find the inverse of the...
 8.81: In Exercises 7982, use the formula below to find the inverse of the...
 8.82: In Exercises 7982, use the formula below to find the inverse of the...
 8.83: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.84: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.85: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.86: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.87: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.88: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.89: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.90: In Exercises 8390, use an inverse matrix to solve (if possible) the...
 8.91: In Exercises 9194,use the matrix capabilities of a graphing utility...
 8.92: In Exercises 9194,use the matrix capabilities of a graphing utility...
 8.93: In Exercises 9194,use the matrix capabilities of a graphing utility...
 8.94: In Exercises 9194,use the matrix capabilities of a graphing utility...
 8.95: In Exercises 9598, find the determinant of the matrix.
 8.96: In Exercises 9598, find the determinant of the matrix.
 8.97: In Exercises 9598, find the determinant of the matrix.
 8.98: In Exercises 9598, find the determinant of the matrix.
 8.99: In Exercises 99102, find all (a) minors and (b) cofactors of the ma...
 8.100: In Exercises 99102, find all (a) minors and (b) cofactors of the ma...
 8.101: In Exercises 99102, find all (a) minors and (b) cofactors of the ma...
 8.102: In Exercises 99102, find all (a) minors and (b) cofactors of the ma...
 8.103: In Exercises 103106, find the determinant of the matrix. Expand by ...
 8.104: In Exercises 103106, find the determinant of the matrix. Expand by ...
 8.105: In Exercises 103106, find the determinant of the matrix. Expand by ...
 8.106: In Exercises 103106, find the determinant of the matrix. Expand by ...
 8.107: In Exercises 107110, use Cramers Rule to solve (if possible) the sy...
 8.108: In Exercises 107110, use Cramers Rule to solve (if possible) the sy...
 8.109: In Exercises 107110, use Cramers Rule to solve (if possible) the sy...
 8.110: In Exercises 107110, use Cramers Rule to solve (if possible) the sy...
 8.111: In Exercises 111114, use a determinant and the given vertices of a ...
 8.112: In Exercises 111114, use a determinant and the given vertices of a ...
 8.113: In Exercises 111114, use a determinant and the given vertices of a ...
 8.114: In Exercises 111114, use a determinant and the given vertices of a ...
 8.115: In Exercises 115 and 116, use a determinant to determine whether th...
 8.116: In Exercises 115 and 116, use a determinant to determine whether th...
 8.117: In Exercises 117120, use a determinant to find an equation of the l...
 8.118: In Exercises 117120, use a determinant to find an equation of the l...
 8.119: In Exercises 117120, use a determinant to find an equation of the l...
 8.120: In Exercises 117120, use a determinant to find an equation of the l...
 8.121: In Exercises 121 and 122, find the uncoded row matrices for the mes...
 8.122: In Exercises 121 and 122, find the uncoded row matrices for the mes...
 8.123: In Exercises 123 and 124, decode the cryptogram by using the invers...
 8.124: In Exercises 123 and 124, decode the cryptogram by using the invers...
 8.125: True or False? In Exercises 125 and 126, determine whether the stat...
 8.126: True or False? In Exercises 125 and 126, determine whether the stat...
 8.127: Under what conditions does a matrix have an inverse?
 8.128: Writing What is meant by the cofactor of an entry of a matrix? How ...
 8.129: Three people were asked to solve a system of equations using an aug...
 8.130: Think About It Describe the rowechelon form of an augmented matrix...
 8.131: Solve the equation for 2 _ _ 3 5 _8 _ _ _ 0
Solutions for Chapter 8: Matrices and Determinants
Full solutions for Precalculus  7th Edition
ISBN: 9780618643448
Solutions for Chapter 8: Matrices and Determinants
Get Full SolutionsPrecalculus was written by and is associated to the ISBN: 9780618643448. Chapter 8: Matrices and Determinants includes 131 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Since 131 problems in chapter 8: Matrices and Determinants have been answered, more than 30663 students have viewed full stepbystep solutions from this chapter.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Amplitude
See Sinusoid.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Horizontal translation
A shift of a graph to the left or right.

Identity properties
a + 0 = a, a ? 1 = a

Index of summation
See Summation notation.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Length of a vector
See Magnitude of a vector.

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Reflection
Two points that are symmetric with respect to a lineor a point.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Xscl
The scale of the tick marks on the xaxis in a viewing window.

Zero vector
The vector <0,0> or <0,0,0>.