{(9,5,6), (3,5,6),(0,0,2), (4,6,0)} is linearly dependent in R'

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

Q: Write v as a linear combination of u, u2, uz, where (a) v = (4, –9, 2), u = (1,2, –1), uz = (1,4,2),…

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Q: Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

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Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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Q: The line through the point (0, 1, 1) that is orthogonal to both ⟨0, -1, 3⟩ and ⟨2, -1, 2⟩.

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Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2) , the robot turns 90°…

A: The robot begins moving at (2,1) and reaches at (5, 2) taking a linear path. So, the equation of a…

Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: 49. The line through the point t (0, 1, 1) that is orthogonal to both (0, -1, 3) and (2, –1, 2).

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Q: Use chain rule to find az at (u, v) = (1, 1) if

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

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Q: find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns…

A: For the solution of the problem follow the next step.

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

A: Introduction: The Gram–Schmidt system is a way for orthonormalizing a fixed of vectors in an…

Q: 4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function…

A: The solution are next step

Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: Linear equation

Q: A robot begins moving on a linear path at (2, 1). When it reaches (5, 2), the robot turns 90°…

A: We have to find the y-coordinate.

Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

A: This is a problem related to linear coordinates. based on the diagram shown in solution we will…

Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

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Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

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Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: Find the flux of ỹ across S.

A: In this question we need to find the flux across the surface is part of sphere of radius 9.

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: The set of vectors u1 = , and u2 = are %3D having rank 3 Linearly independent having rank 1…

A: Given- The set of vectors u1=<1,-1,3,-1> and u2=<1,-1,4,2> To Check- If they are…

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

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Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: Show the process of Reflecting a vector/matrix about a line that goes through the origin?

A: Reflection of vector/matrix about a line that goes through the origin: When we reflex a point about…

Q: Suppose div(F(5,3,2)) = 240. Estimate the flux of F out of a small, outward-oriented box of side…

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Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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Q: 3. Prove or disprove that the system of vectors [-1,1, 2], [2, –3, 1], [10, – 1,0] is linearly…

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Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

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.