Use the indicated entry as the pivot and perform the pivoting. X1 X2 X3 $1 $2 $3 z 1 1 1 1 140 3 1 0 0 0 60 1 0 0 160 2 30 0 1 0 200 0 0 1 0 1-1-4 0 X₁ X2 X3 S₁ S2 S3 Z …..

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Vectors u and v are shown in the graph. -12 -11 -10 -9 -8-7-6 -5 -4-3-2 What is projvu? u 6 5 3 2 -1…

A: Graph

Q: The vectors (2, 4, –6), (2, –6, 4) and (4, –2, 10) are linearly Select one: O A. independent O B.…

A: We have to state whether the given vectors are linearly independent.

Q: 5. Determine whether the set of vectors are linearly de- pendent or independent. Explain results…

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Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

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Q: Given the [1 2 2 024 00 0-1 diagonalization, fill in the blacks 1 2 1] I Y 30 X= -1 0 0 0 0 16 0 20…

A: we have given the diagonalization of the matrixWe need to find the value of the x, y, z and w

Q: (b) Write the following vectors as linear combinations of 21, 22, and 23.

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Q: The value of i1/3) in cartesian coordinates is a. (V3 + i)/2 b. -(V3+ i)/2 c. (V3 – i)/2 d. none of…

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Q: 1 %Define the three vectors u=[1, 0, -4], v=[3, -3, 1], and w=[0, 2, 1]. u=[1 0 -4] v=[3 -3 1] w= [0…

A: ##Importing the library of numpy and then Defining the 3 vectors : import numpy as np…

Q: Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be…

A: Let V=v1, v2,...,vp∈ℝn x1v1+x2v3+..+xpvp=0 is Linearly independent if x1=x2=..=xp=0 Since the…

Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

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Q: Let D4 = {1, a, a², a³, b, ab, a²b, a³b} and X = {1, a, a²,a³}. Find i. Centralizer ofX. ii. Center…

A: Step:-1 Centralizer (C):- The centralizer of a set say S of a group say G,  is a subgroup of group G…

Q: For the matrix H = Answer: 1 2 -1 2 0 51 13 find three different non-zero vectors that are in the…

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Q: Given u = , v = -5i - j, and w (AB) is defined by the points (1, 6) and (-2, 8). a Find v in…

A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into…

Q: Which of the following sets is linearly independent? M={ (1,1,3),(3, 2, 0), ( 4 , 5 , 6 )} O…

A: x,y,z  are linearly independent if for linear combination ax+by+cz=0, have unique solution, that is…

Q: 1. a. The points (3,-1,2) and (-1,3,-4) are the endpoints of a diameter of a sphere i. Determine the…

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Q: Consider the subset of P3 Q = {−6x² + 4x − 6, −24x² + sx + 6, 2sx + s} Find the two values of s for…

A: In this question, we will find the values of 's' for which a given set is linearly dependent.

Q: solve using the concept of rank.

A: Given set of vectors is: S = {[4     1     2], [2      5      -5], [2      -1        3]} We have to…

Q: The vectors are linearly independent if and only if k # 3 ·020 v= -3 -16+ k u= 7 22 W =

A: We know that if the vectors are linearly independent then their determinant is not 0. So,…

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: Choose the pivot column: 4230 20000 SI 1 0 1 0 2 1 -4 0 -3 0 0 20000 Column 1 Column 2 Column 3…

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Q: Given the points (-1, 3), (0, 1), (1, 3), and (2, 9), solve the equation Ax = b for x = c de to find…

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Q: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

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Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

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Q: Write, in your notebook, which vectors are represented in the Cartesian plane.

A: We know that, the position vector AB → between the points Ax1,y1 and Bx2,y2 is given by  AB→=x2-x1…

Q: give vector form for the solution

A: Here we have to find the vector form

Q: Find the vectors T, N, and B at the given point 16 r(c) = (1², 31², c), (4, 15, 2) T = N = B =

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Q: an example of a (nonzero) vector perpendicular to ?⃗ = ⟨−17, 3, −6⟩. Please give full explanation…

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Q: Which of the following sets of vectors are linearly independent? or 12 4 -14 -2 6 22 -8 3 -21 2 O…

A: 1. 3 vectors in 4-dimensional space are always dependent. 2. Vectors are said to be independent if…

Q: A. Which of the following points would lie in the cone of the three vectors v1 =(0,5,0), v2 =(4,0,0)…

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Q: Rotate Quadrilateral VWXY 180o about the origin. v (-5,-2) w(-2,-1) x(1,-6) y(-7,-7)

A: To find- Rotate the Quadrilateral vwxy 180° about the origin. v = -5, -2w = -2, -1x = 1, -6y = -7,…

Q: Calculate the cross product. (i - 9j + 6k) x (j – k)

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