write v as a linear combination of u1, u2, u3, if possible. v=(2,5,-4,0), u1=(1,3,2,1), u2=(2,-2,-5,4), u3=(2,-1,3,6)

Q: Find u - v, u · u, ||v||², (u - v)v, and u - (3v). u = 4i + j - 2k, v = i - 3j + 2k (a) u: v (b) u.…

A: Dot product of two vector is - a→=  a1i^ +  a2j^ +  a3k^ b→=  bi^ +  b2j^ +  b3k^ a→.b→ =  a1 b1 +…

Q: Solve for w where u = (0, 1, 1, –1) and v = (3, 0, –1, 2). %3D w + 2v = -4u W =

A:

Q: Determine whether the set S=(U,V,W) are linearly independent or linearly dependent. Where, U=…

A:

Q: Determine if b is a linear combination of a1, a2, and a3 a1 a2 a3 b 1 -2 -6 11 0 3 7 -5 1…

A: It is given that b is a linear combination of a1, a2, and a3.

Q: Write v as a linear combination of u,, u,, and u,, if possible. (Enter your answer in terms of u,,…

A:

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A:

Q: Find an equation of the line that passes through the given points. (Let x be the independent…

A: Given:The line passes through the points (2,2) and (3,7).The equation of the line is of the form,

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: We want to find linearly dependent vectors. We know that a set of vectors is said to be linearly…

Q: Determine whether a=(2,-2,4), b=(3,5,4) and c=(0,1,1) are linearly dependent or not?

A:

Q: Write v as a linear combination of u, u2, and u3, possible. (If not possible, enter IMPOSSIBLE.) =…

A: We will find out the required value.

Q: 15 |ム=() -40 -30 -20 -10. -5 10 10 -10 15 (8)

A: We have,  x1=-5, 5 and x2=2,-2 This can be done as follows:

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A:

Q: Q/ What is the cross product of a = (-2, 3, 5) and b = (-4, 1, -6)? a, = -2, a, = 3 and a, = 5 b, =…

A:

Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

A:

Q: Write v as a linear combination of u,, u2, and uz, if possible. (Enter your answer in terms of u,,…

A: the given vectors v=-1, 7, 2, u1=2,1,5, u2=3,-1,5, u3=-2,1,-3

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A:

Q: write v as a linear combination of u,, u„ and u̟, if possible. Uz3 47. v = (10, 1, 4), u, = (2, 3,…

A:

Q: Use the translation (z, y)-> (z- 8, y+4) to find the image of A (-2, 6). O A (10, -10) O A'(-10, 10)…

A:

Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

A:

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in R.…

A:

Q: Write v as a linear combination of u1, u2, and u3, if possible. (If not possible, enter IMPOSSIBLE.)…

A:

Q: a) Write w = (−1, 1, 19) as a linear combination of v 1 = (1, −1, 0), v 2 = (3, 2, 1) and v 3 = (0,…

A: In this question we will use basic of algebra i.e first we will assume arbitrary constants a, b, c…

Q: Write v as a linear combination of u1, U2, and u3, if possible. (If not possible, enter IMPOSSIBLE.)…

A:

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: Set of vectors x1, x2, ...xk is independent vectors if for scalar a1, a2,..., an.…

Q: . v=(0,5,3,0), u1=(1,1,2,2), u2=(2,3,5,6), u3=(-3,1,-4,2)

A: NOTE: As per Bartleby rules only one question will be answered. Please upload others separately.…

Q: Find u · v, u· u, ||v||², (u · v)v, and u (3v). u = (2, 10), v = (-3, 2) %3D (a) U V (b) U U (c)…

A:

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A:

Q: Which of the following sets of vectors in R3 are linearly dependent? Note. Mark all your choices.…

A: We have to find which of the sets are linearly dependent.

Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

A:

Q: Exercise:- Let A = -2 -2 and us U: Find L,U s.t A: LU

A: The given matrix is: A=253-1467163-23214-2

Q: Write the vector 3 (if it is possible) as a linear combination of the vectors d1, d 2.

A:

Q: Which of the following subsets are linearly independent ? B = {(2,1), (-3,-2), (9, 11)} %3D B2 =…

A: We have to check each one by one.

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A:

Q: Find u - v, 2(u + 3v), and 2v - u. | u = (4, 0, -2, 5), v = (0, 6, 5, 4) %3D (a) u – v = (b) 2(u +…

A:

Q: Find ||u||, ||v||, and ||u + v||. (1, -2, 0, 2), v = (0, 3, 2, 1) u = (a) ||u|| (b) ||v|| (c) ||u +…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find u · v, u · u, || V||^2, ( u • u )v, and u • (3v). u= , v= (a) u•v   (b) u•u   (c) ||v||^2…

A:

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A:

Q: Find ||u||, ||v||, u-v, and d(u, v). u = (-1, 3), v = (3, 4) (a) ||u|| (b) ||v| (c) u. V (d) d(u, v)

A: We have to find u , v , u·v , and d(u, v) where u=(-1, 3) and v=(3, 4) .

Q: In writing v as a linear combination of u,,u, &u, (if possible) given: v = (3,0, – 6), u.= (1. –…

A: We have written as linear combination of

Q: Plot the points A(5, -2), B(-5, -2), C(5, 2), D(-5, 2), E(3, 0), and F(0, 3) on a coordinate plane.

A: To plot the points A(5,-2), B(-5,-2), C(5,2), D(-5,2), E(3,0), F(0,3)

Q: Solve for w where u (0,-1, 1, 1) and v (2, 3, 0, -1). %3D %3D w + 2v = -4u W =

A:

Q: Which set of ordered pairs (x, y) could represent a linear function? А %3 {(-4,5), (-1,-1), (0, -3),…

A: Given sets of ordered pairs are A={(-4, 5), (-1, -1), (0, -3), (1, -6)} B={(2, -5), (4, -3), (7,…

Q: Find u × v, v × u, and v × v. u = v =

A: The two vectors a→=⟨a1,a2,a3⟩and b→=⟨b1,b2,b3⟩, then the cross product is given by the formula,…

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: We want to find linear dependent vectors.

Q: Write v as a linear combination of u1, u2, and u3, if possible. 1. u1=(1,1,2,2), u2=(2,3,5,6),…

A: Given: v=0,5,3,0 , u1=1,1,2,2, u2=2,3,5,6 , u3=-3,1,-4,2 To determine: vas a linear combination of…

Q: Write v as a linear combination of u,, u,2, and u,, if possible. (Enter your answer in terms of u,,…

A:

Q: write v as a linear combination of u1, u2, u3, if possible. v=(0,5,3,0), u1=(1,1,2,2),…

A:

Q: (1, 2), (2, 3), (6, 0) are linearly independent

A: If one of the vector can be  written as the linear combination of remains vectors then these are…

Q: Find x so that (-2, 3), (x, 6), and (8, 8) are collinear.

A: Colinear:  For (-2,3),(x,6),(8,8) are colinear. -231x61881=0

Q: Let u = (-3, 1, 7), v = (3,0, -6), and w = (6, -1, –3) Find the components of v – w. (-4, 1, 3) V -…

A: Given u = (- 3, 1, 7), v = (3, 0, - 6) , and w = (6, - 1, - 3) Find the components of v — w.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.