1,959 Answered Questions for the topic linear algebra

Linear Algebra Math Algebra 1 Calculus

09/20/21

Piecewise linear functions
Derek earns $25 per hour (or part of an hour) for a regular 40-hour work week. Sometimes, he works over 40 hours a week and earns “double time” for the extra hours worked. (That means that his... more
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Linear Algebra

09/16/21

Linear Algebra Transformations
The linear transformation T : R2 → R2 given by T (x) =[3 42 3]x is one-to-one and onto.Let ~b =[cd]. Find the unique vector x so that T (b) = x. (The entries of x will be expressed interms of c and... more
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Linear Algebra

09/15/21

When using partial fractions to find antiderivatives in calculus we decompose complicated rational expressions into the sum of simpler expressions that can be integrated individually.

The required decomposition is 64/(x(x^2+8))=(A/x)+(Bx+C)/(x^2+8) Find the values of the missing constants. A= 8 B= -8 C= ?
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Linear Algebra

09/15/21

Find a polynomial of the form f(x)=ax^3+bx^2+cx+d such that f(0)=−5, f(−2)=6, f(4)=5, and f(−5)=−3. f(x) = ?
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Linear Algebra

09/15/21

Determine all values of h and k for which the system has no solution.
−3x-3y=h-4x+ky=-1k = ?h ≠ ?
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Linear Algebra

09/11/21

The quotient of a number and -5,increased by 7 is at minimum 1
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Linear Algebra

09/10/21

Need Help with HW Problem
https://imgur.com/a/W3bCpeP [Link to problem and my solution thus far]I am pretty sure I found the distance correctly. For the second part, although I think it's right, I'm hesitant because it... more
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09/09/21

Linear Differential Equations
Find the particular antiderivative that satisfies the following conditions:dx/dt=4e(^t)−2; x(0)=7.I know dx/dt of 4e^(t)-2 is 4e^(t)-2t, but I do not know what to do with the x(0)=7.
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Linear Algebra

09/02/21

Systems of Linear Equations using row echelon form. Need help with Part 2.
Part 1: Verify that the following augmented matrices are in rref(row echelon form), identify the leading and the freevariables, then find all the solutions, if there are any, to the systems of... more
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Linear Algebra

08/31/21

Find a basis of subspaces U and W
U = {(x1, x2, x3, x4) ∈ R 4 | x2 − x4 = 0 ∧ x1 = 0} ;W = {(x1, x2, x3, x4) ∈ R 4 | x2 = 0 = x3} ; Find a basis of subspaces U and W. Are the 2 subspaces complement to one another?Find a base of... more
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Linear Algebra

08/28/21

Solve the inequality and explain the meaning of the solution
A meteorologist announces that yesterday’s high temperature was within 4° Celsius of 18° Celsius all across the country. Write an inequality that involves an absolute value to represent yesterday’s... more
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Linear Algebra Algebra 2 Parabola

08/26/21

Plot the points on the graph of f(x)=1/4(x+6)^2-5 that corresponds to x -values of -2 and -4 then plot the vertex and the reflections of these points in the axis of symmetry
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Linear Algebra Math Algebra 1 Calculus

08/25/21

Vectors and the Geometry of Space
Consider the line L(t)=⟨4−3t,17+4t⟩. Then L intersects:1.The x-axis at the point.... when t =...2.The y-axis at the point..... when t =....3.The parabola y=x2 at the points..... and... when t... more
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Linear Algebra Calculus Precalculus Vector

08/23/21

Find a vector v such that ||v||=5 and v is in the same direction as i+4j .
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Linear Algebra Linear Equations

08/20/21

Linear equations word problem
A community center offers a 1-day craft show where people can rent booths to sell their hand-made goods.the community center charges $85 and an additional $15 per booth a person rents.(a) create an... more
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Linear Algebra

08/09/21

Determine the equation of the plane passing through the points A(4,1,1) B(0,0,5) and C(2,7,2)
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/02/21

write the following numbers in a +bi form

A. (4+4i)/(-4+4i)=B. -3/3i + -4/2i=C. (5i)^3 =
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

So the distance from 𝑃=(5,−4,4) P = ( 5 , − 4 , 4 ) to the line through the points 𝐴=(2,5,1) A = ( 2 , 5 , 1 ) and 𝐵=(5,4,−2) B = ( 5 , 4 , − 2 ) is
the distance d of a point P to the line through the points A and B is the length of the component of AP that is orthogonal to AB So the distance from 𝑃=(5,−4,4) P = ( 5 , − 4 , 4 ) to the line... more
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are

Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are ????
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are

Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are ????
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

Suppose 𝐵=(8,4) B = ( 8 , 4 ) and 𝐴𝐵−→−=⟨15,1⟩ A B → = ⟨ 15 , 1 ⟩ . Then

Suppose 𝐵=(8,4) B = ( 8 , 4 ) and 𝐴𝐵−→−=⟨15,1⟩ A B → = ⟨ 15 , 1 ⟩ . Then A= ??
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

So the distance from 𝑃=(3,−3,3) P = ( 3 , − 3 , 3 ) to the line through the points 𝐴=(−1,−4,0) A = ( − 1 , − 4 , 0 ) and 𝐵=(−3,0,−1) B = ( − 3 , 0 , − 1 ) is

The distance  of a point  to the line through points  A and B is the length of the component AP of  that is orthogonal to AB, as indicated in the diagram.So the distance from 𝑃=(3,−3,3) P = ( 3 , −... more
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

Find the distance the point P(-2, 2, 3), is to the plane through the three points Q(-1, 0, 2), R(1, -2, 5), and S(-3, -2, 4).

Find the distance the point P(-2, 2, 3), is to the plane through the three points Q(-1, 0, 2), R(1, -2, 5), and S(-3, -2, 4).
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Linear Algebra Algebra 1 Algebra 2 Prealgebra

08/01/21

Find the point at which the line ⟨−2,−2,0⟩+𝑡⟨−3,2,−1⟩ ⟨ − 2 , − 2 , 0 ⟩ + t ⟨ − 3 , 2 , − 1 ⟩ intersects the plane −3𝑥+2𝑦−2𝑧=62 − 3 x + 2 y − 2 z = 62 .

Find the point at which the line ⟨−2,−2,0⟩+𝑡⟨−3,2,−1⟩ ⟨ − 2 , − 2 , 0 ⟩ + t ⟨ − 3 , 2 , − 1 ⟩ intersects the plane −3𝑥+2𝑦−2𝑧=62 − 3 x + 2 y − 2 z = 62 .
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Linear Algebra Algebra 1 Algebra 2 Algebra

08/01/21

Find the point at which the line ⟨0,4,−4⟩+𝑡⟨4,5,−3⟩ ⟨ 0 , 4 , − 4 ⟩ + t ⟨ 4 , 5 , − 3 ⟩ intersects the plane −𝑥+𝑦+𝑧=−10 − x + y + z = − 10 .

Find the point at which the line ⟨0,4,−4⟩+𝑡⟨4,5,−3⟩ ⟨ 0 , 4 , − 4 ⟩ + t ⟨ 4 , 5 , − 3 ⟩ intersects the plane −𝑥+𝑦+𝑧=−10 − x + y + z = − 10 .
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