- 6-184.108.40.206: Use Definition 6.14 to compute the determinants of the following ma...
- 6-220.127.116.11: Use Definition 6.14 to compute the determinants of the following ma...
- 6-18.104.22.168: Repeat Exercise 1 using the method of Example 2.
- 6-22.214.171.124: Repeat Exercise 2 using the method of Example 2.
- 6-126.96.36.199: Find all values of that make the following matrix singular. A = 1 1...
- 6-188.8.131.52: Find all values of that make the following matrix singular. A = 1 2...
- 6-184.108.40.206: Find all values of so that the following linear system has no solut...
- 6-220.127.116.11: Find all values of so that the following linear system has an infin...
- 6-18.104.22.168: Use mathematical induction to show that when n > 1, the evaluation ...
- 6-22.214.171.124: Let A be a 3 3 matrix. Show that if A is the matrix obtained from A...
- 6-126.96.36.199: The solution by Cramers rule a11x1 + a12 x2 + a13x3 = b1, a21x1 + a...
- 6-188.8.131.52: Prove that AB is nonsingular if and only if both A and B are nonsin...
- 6-184.108.40.206: a. Generalize Cramers rule to an n n linear system. b. Use the resu...
Solutions for Chapter 6-4: The Determinant of a Matrix
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Addition property of inequality
If u < v , then u + w < v + w
The farthest point from the Sun in a planet’s orbit
The factor Ae-a in an equation such as y = Ae-at cos bt
Distance (on a number line)
The distance between real numbers a and b, or |a - b|
The number found when the corresponding components of two vectors are multiplied and then summed
Any solution of the resulting equation that is not a solution of the original equation.
The line through the focus and perpendicular to the directrix of a conic.
The difference between the third quartile and the first quartile.
Inverse cosine function
The function y = cos-1 x
Left-hand limit of f at x a
The limit of ƒ as x approaches a from the left.
Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ
A local maximum or a local minimum
Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
The process of fitting a polynomial of degree n to (n + 1) points.
Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0
Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.
The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.
Set of all possible outcomes of an experiment.
A real number.
A special form for a system of linear equations that facilitates finding the solution.