Explanation Given: Statement is given as “In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.” Calculation: Statement is given as “In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.” Consider the system of linear equations having graphs of two linear equations...

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11.1, Problem 6VRVC

To determine

To complete the below statement:

“In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.”

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 5VRVC

Chapter 11.1, Problem 1ES

Students have asked these similar questions

1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.

Question 3 over a field K. In this question, MË(K) denotes the set of n × n matrices (a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is equivalent to A-¹? Justify your answer. (b) Let B be given by 8 B = 0 7 7 0 -7 7 Working over the field F2 with 2 elements, compute the rank of B as an element of M2(F2). (c) Let 1 C -1 1 [4] [6] and consider C as an element of M3(Q). Determine the minimal polynomial mc(x) and hence, or otherwise, show that C can not be diagonalised. [7] (d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write down all the eigenvalues. Show your working. [8]

R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

Chapter 11 Solutions

EBK ALGEBRA FOUNDATIONS

Ch. 11.1 - Prob. 1VRVC Ch. 11.1 - Prob. 2VRVC Ch. 11.1 - Prob. 3VRVC Ch. 11.1 - Prob. 4VRVC Ch. 11.1 - Prob. 5VRVC Ch. 11.1 - Prob. 6VRVC Ch. 11.1 - Prob. 1ES Ch. 11.1 - Prob. 2ES Ch. 11.1 - Prob. 3ES Ch. 11.1 - Prob. 4ES

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

To complete the below statement: “In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.”

Solution Summary: The author explains that in a system of linear equations in two variables, if the graph is different, the equation is independent.

Videos

To complete the below statement: “In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.”

Want to see the full answer?

Chapter 11 Solutions

To complete the below statement:

“In a system of linear equations in two variables, if the graph of the equations are different, the equations are ____________ equations.”