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Linear Algebra

05/29/23

Linear programming

Consider an LP in standard form with feasible region S, and constraints Ax = b and x ≥ 0component-wise. Recall that a nonzero vector d is a direction of unboundedness if ∀s ∈ S, c ≥ 0,x + cd ∈ S.... more

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Linear Algebra

05/28/23

Compute the product C ⃗s , and show that it is equal to the linear combination of ⃗c1, ⃗c2, and ⃗c3 with coefficients a, b, and c.

Let c1, ⃗c2, ⃗c3, and ⃗s be the columns given below. Let C be the matrix C = [ ⃗c1 ⃗c2 ⃗c3]. That is, C is the matrix with columns ⃗c1, ⃗c2, and ⃗c3, in that order. ⃗c1 = [1] [2] [3] ⃗c2 = [0]... more

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Linear Algebra

05/28/23

For values of a and b for which the system is consistent, find its general solution and express your answer in the usual column form.

Consider the system of equations with the following augmented matrix, in which a and b are real numbers. (1 0 2 a^2 3| b) (0 a b 0 1| a) (0 0 0 a 0| b^2-1)(b) For values of a and b for which the... more

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Linear Algebra

05/28/23

Find all values of a and b for which the system is inconsistent.

Consider the system of equations with the following augmented matrix, in which a and b are real numbers. (1 0 2 a^2 3| b) (0 a b 0 1| a) (0 0 0 a 0| b^2-1) (a) Find all values of a and b for which... more

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Linear Algebra

05/21/23

Solving a distance, rate, time, problem using a system of linear

A motorboat travels 308 kilometers in 7 hours going upstream. It travels 490 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate... more

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Linear Algebra

05/21/23

Solving a distance, rate, time problem using a system of linear

Two buses leave a station at the same time and travel in opposite directions. One bus travels 16km/h slower than the other. If the two buses are 786 kilometers apart after 3 hours, what is the rate... more

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Linear Algebra

05/20/23

Find (x ,y) such that (x, y, 1, -2) are coefficients for a dependence relation for m1, m2, m3, m4.

Letm1 = (1 1) m2 =(1 2) m3 = (1 3) m4 = (3 2) 1 1 2 3 3 5 2 1Find (x ,y) such that (x, y, 1, -2) is a dependence relation for m1,... more

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Linear Algebra

05/15/23

The sum of two numbers is 42. One number is 2 times as large as the other. What are the numbers

Find the larger and smaller number.

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Linear Algebra

05/14/23

Represent the set {(a − b, b − c, c − a) | a, b, c ∈ R} ⊂ R 3

Represent the set {(a − b, b − c, c − a) | a, b, c ∈ R} ⊂ R 3 as Span{v1, v2, v3} for some vectors v1, v2, v3. Prove that this set is a subspace of R3.

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Linear Algebra

05/14/23

Let V denote the set of all ordered pairs (x, y) and define addition in V as in R2

Let V denote the set of all ordered pairs (x, y) and define addition in V as in R2. However, define a new scalar multiplication in V by a (x, y) = (ay, ax). Determine if V is a vector space with... more

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Linear Algebra Math Algebra 1 Algebra 2

05/12/23

The location, given in polar coordinates, of two planes are (5 mi, 14°) and (3 mi, 65°). Find the distance between the airplanes

The location, given in polar coordinates, of two planes are (5 mi, 14°) and (3 mi, 65°). Find the distance between the airplanes. (Simplify your answer. Round the final answer to three... more

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Answers •3

Linear Algebra Math Algebra 1 Algebra 2

05/12/23

Use an algebraic method to find the angle between the vectors. Use a calculator to approximate exact answers when appropriate. u=<−15,−8> and v=<-1,5> (Round to three decimal places as needed.)

Use an algebraic method to find the angle between the vectors. Use a calculator to approximate exact answers when appropriate. u=<−15,−8> and v=<-1,5> (Round to three decimal places... more

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Linear Algebra Math Algebra 1 Algebra 2

05/12/23

An airplane is flying on a compass heading (bearing) of 330° at 320 mph. A wind is blowing with the bearing 300° at 40 mph.

An airplane is flying on a compass heading (bearing) of 330° at 320 mph. A wind is blowing with the bearing 300° at 40 mph. (a) Find the component form of the velocity of the airplane.... more

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Linear Algebra Math Algebra 1 Algebra 2

05/12/23

Find the vector projection of u onto v. Then write u as the sum of two orthogonal vectors, one of which is projvu. u=〈−2,3〉, v=〈5,6〉

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Linear Algebra Math Algebra 1 Algebra 2

05/12/23

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (−5,5) and (3,5), transverse axis endpoints (−4,5) and (2,5).

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Answers •2

Linear Algebra Math Algebra 1 Algebra 2

05/12/23

Find an equation in standard form for the ellipse that satisfies the given conditions. Minor axis endpoints (0,±5), major axis length 14

Find an equation in standard form for the ellipse that satisfies the given conditions.Minor axis endpoints (0,±5), major axis length 14

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Answers •2

Linear Algebra Math Algebra 1 Algebra 2

05/12/23

Prove that the graph of the equation is a parabola, and find its vertex, focus, and directrix. x^2+2x−y+2=0

Prove that the graph of the equation is a parabola, and find its vertex, focus, and directrix.x^2+2x−y+2=0

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Linear Algebra Math

05/06/23

What is the significance of eigenvalues and eigenvectors in linear algebra, and how are they used in real-world applications?

What is the significance of eigenvalues and eigenvectors in linear algebra, and how are they used in real-world applications?how these are different from each other ?

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Linear Algebra

05/02/23

Needing an equation that describes the relationship between three variables

I have three variables that have a specific relationship with each other. I know what they need to do at specific points, but I need to find out the values in between, and I need an equation that... more

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Linear Algebra

04/30/23

For which values of a and b does the system have a unique solution?

Given the system of equationsx+z=3ax+y=23x + y + bz = 7

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Linear Algebra Algebra 1 Algebra 2 Prealgebra

04/29/23

Algebra Question. (Two-way) Concept.

If -24 = 3(1+r) what is the value of 7(1+r) I am practicing for the SAT on Khan Academy, and this was one of the questions that showed up. The answer I got was -56, which was the correct answer,... more

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Linear Algebra Math Algebra 1 Algebra 2

04/29/23

Find an equation in standard form for the hyperbola that satisfies the given conditions. Transverse axis endpoints, (1,5) and (7,5), slope of one asymptote 4/3.

Find an equation in standard form for the hyperbola that satisfies the given conditions. Transverse axis endpoints, (1,5) and (7,5), slope of one asymptote 4/3. (Simplify your answer. Type... more

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Answers •1

Linear Algebra Math Algebra 1 Algebra 2

04/29/23

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (0,±15), transverse axis length

Find an equation in standard form for the hyperbola that satisfies the given conditions.Foci (0,±15), transverse axis length (Type an equation. Type your answer in standard form.)

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Answers •1

Linear Algebra

04/25/23

Linear algebra Eigens

Find a 2x2 matrix A for which E-5 = span {[-3,1]} , E-4 = span {[5,-2]}Where Eλ denotes the eigenspace associated with the eigenvalue λ.

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Linear Algebra

04/25/23

Linear algebra help

let M = Find formulas for the entries of M^n, where n is a positive integer.

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Linear programming

Compute the product C ⃗s , and show that it is equal to the linear combination of ⃗c1, ⃗c2, and ⃗c3 with coefficients a, b, and c.

For values of a and b for which the system is consistent, find its general solution and express your answer in the usual column form.

Find all values of a and b for which the system is inconsistent.

Solving a distance, rate, time, problem using a system of linear

Solving a distance, rate, time problem using a system of linear

Find (x ,y) such that (x, y, 1, -2) are coefficients for a dependence relation for m1, m2, m3, m4.

The sum of two numbers is 42. One number is 2 times as large as the other. What are the numbers

Represent the set {(a − b, b − c, c − a) | a, b, c ∈ R} ⊂ R 3

Let V denote the set of all ordered pairs (x, y) and define addition in V as in R2

The​ location, given in polar​ coordinates, of two planes are (5 mi, 14°) and (3 mi, 65°). Find the distance between the airplanes

Use an algebraic method to find the angle between the vectors. Use a calculator to approximate exact answers when appropriate. u=<−15,−8> and v=<-1,5> ​(Round to three decimal places as​ needed.)

An airplane is flying on a compass heading​ (bearing) of 330° at 320 mph. A wind is blowing with the bearing 300° at 40 mph.

Find the vector projection of u onto v. Then write u as the sum of two orthogonal​ vectors, one of which is projvu. u=〈−2​,3〉​, v=〈5​,6〉

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci ​(−5​,5​) and ​(3​,5​), transverse axis endpoints ​(−4​,5​) and ​(2​,5​).

Find an equation in standard form for the ellipse that satisfies the given conditions. Minor axis endpoints ​(0,±5​), major axis length 14

Prove that the graph of the equation is a​ parabola, and find its​ vertex, focus, and directrix. x^2+2x−y+2=0

What is the significance of eigenvalues and eigenvectors in linear algebra, and how are they used in real-world applications?

Needing an equation that describes the relationship between three variables

For which values of a and b does the system have a unique solution?

Algebra Question. (Two-way) Concept.

Find an equation in standard form for the hyperbola that satisfies the given conditions. Transverse axis​ endpoints, (1​,5​) and (7​,5​), slope of one asymptote 4/3.

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (0,±15)​, transverse axis length

Linear algebra Eigens

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The location, given in polar coordinates, of two planes are (5 mi, 14°) and (3 mi, 65°). Find the distance between the airplanes

Use an algebraic method to find the angle between the vectors. Use a calculator to approximate exact answers when appropriate. u=<−15,−8> and v=<-1,5> (Round to three decimal places as needed.)

An airplane is flying on a compass heading (bearing) of 330° at 320 mph. A wind is blowing with the bearing 300° at 40 mph.

Find the vector projection of u onto v. Then write u as the sum of two orthogonal vectors, one of which is projvu. u=〈−2,3〉, v=〈5,6〉

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (−5,5) and (3,5), transverse axis endpoints (−4,5) and (2,5).

Find an equation in standard form for the ellipse that satisfies the given conditions. Minor axis endpoints (0,±5), major axis length 14

Prove that the graph of the equation is a parabola, and find its vertex, focus, and directrix. x^2+2x−y+2=0

Find an equation in standard form for the hyperbola that satisfies the given conditions. Transverse axis endpoints, (1,5) and (7,5), slope of one asymptote 4/3.

Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (0,±15), transverse axis length