Suppose the solution set of a certain system of linear equations can be described as x, = 4+4x2, xX, = - 5 – 7×2, with x, free. Use vectors to describe this set as a line in R3. Geometrically, the solution set is a line through (4, –5,0) parallel to (4, – 7,1)|

Q: Find an equation of the plane through the three points given: = (5,0,0) , Q = (9, 1, 3) , R= (8, 4,…

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Q: Find the equation of the plane through the points (2,-1,3), (2,0,–-1),and (0,7,2).

A: Given that three points and we find that equation of plane . Here i attached solution of this…

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: Compute the system of linear equations using a. elimination using addition or subtraction…

A: Given system of linear equations 3x-9z=33                        (1)7x-4y-z=-15…

Q: Consider the system Jax + by = c lazx + bzy = c2. Use Cramer's Rule to prove that if the first…

A: Given system of equations are, a1x+b1y=c1a2x+b2y=c2 Using Cramer rule to find the solution of the…

Q: If the vectors a=(2,5,-1) and b3(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: Consider the system of equations below = 0 X1 – 2x1 – x3 + 3x4 -2x1 + 4x2 + 5x3 - 5x4 3x1 – 6x2 –…

A: Topic : Linear algebra  As per our guidelines, At a time only one question will be answered.

Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: Suppose the solution set of a certain system of linear equations can be described as x, =6+4x3, X2 =…

A: Given equations are

Q: 1. Verify whether the vector X is a solution of the given system where 2. X' = X; X=

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Q: 1. Verify whether the vector X is a solution of the given system where X; X =| 3 X' =

A: Given:

Q: I can't find a way to solve this practice problem. Can you work it out so I can see how it's done?…

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Q: In each case, find the linear combination of the first two vectors that is as close as possible to…

A: Both part of the question can be converted into the question based on least squares solution of a…

Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Given :                To find the distance of a point in the 3-D system from the origin

Q: Verify whether the vector X is a solution of the given system where 2. X' X; X: %3D 1 0

A: The given differential equation is X'=2110X. Note that, X=13 et+4-4…

Q: Are the vectors-3- 12z-4r, - 2-7z- 2x and -3- 10z - 3z linearly independent? choose If the vectors…

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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: Describe all solutions of Ax= 0 in parametric vector form, where A is row equivalent to the given…

A: The solutions are x1=3x4, x2=8+x4, x3=2-5x4 and x4 is free. Write the solution as a column vector.…

Q: Suppose the solution set of a certain system of linear equations can be described as x, = 4 +4xą, x,…

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Q: Use Cramer’s Rule to solve (if possible) the system of linear equations.

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Q: 4- Find an equation of the plane that passes through the given points (-2, 1, 1), (0, 2, 3), and (1,…

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Q: 1. Verify whether the vector X is a solution of the given system where 2. X'= X; X = e'+ %3D

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Q: Suppose the solution set of a certain system of linear equations can be described as x, = 8+ 5x3, X…

A: Given that  The solution set of a certain system of linear equations can be described as  x1=8+5x3…

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: 1. Find a set of homogeneous linear equations whose solution space is generated by the vectors: а.…

A: By using rref of matrix we solve the given problem as follows :

Q: Use Cramer’s Rule to solve (if possible) the system of linear equations.

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Q: The vector (1,-2, –6) is a solution of the linear system: X1 + 4x2 – 4x3 = 21 5x1 + 18x2 – 18x3 = 95…

A: Explanation of the answer is as follows

Q: Find an equation for the plane through А (0, 0, 1), B (2, 0, 0), and С (), 3, 0).

A: The equation of a plane passing through three points Ax1, y1, z1, Bx2, y2, z2 and Cx3, y3, z3 is…

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: Verify that the vector X is a solution of the given homogeneous system. 1 -1 x-( )xx-(7)** X'= 4 X;…

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Q: Find the linear equation of the plane through the origin and the points (6, 4, 2) and (6, –1, 1).

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Q: Use Cramer's rule to solve the following system of linear equations. 4x + 9y + 12z = -1, 3x +y + 16z…

A: Consider the system of equations: a1x+b1y+c1z=d1a2x+b2y+c2z=d2a3x+b3y+c3z=d3   Using Cramer's rule,…

Q: P, - Solve the foilowing System of Linear equet;'on by Gaujs elimintion metlod :.. X, -X2 +3X3 =10…

A: Gauss elimination method basically convert an augumented matrix of a system of linear equations into…

Q: Find the maximum value of Q(x) = 7x} + 3x – 2x1x2, subject to the constraint xỉ + x = 1. (Do not go…

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Q: Write the vector (7, 8, -8) as a linear combination (if possible) as of the vectors (-1, 1, 2), (2,…

A: Let the linear combination be, x-112+y23-2=78-8 It is required to determine the value of 'x' and 'y'…

Q: Find the vector form for the geveral selution to the system of equations. X, - X, + Zxg - xy - Xx=-8…

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Q: Find an equation for the plane passing through the points (– 5, 2, 3), ( – 1, 2, 5), and (– 2, – 3,…

A: We have to find equation of plane Passing through 3 points.

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: The vector (8, 0, 1) is a solution of the linear system: X1 + 4x2 – 4x3 = 4 5х1 + 16х2 — 16х; — 24…

A: Linear equation: - Linear equations are simply another class of "equations." Linear equations will…

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: In this question, we verify X1 and X2 are the solution and then we find the wronskian to check the…

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Compute the system of linear equations using a. elimination using addition or subtraction…

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Q: Find the component form of the vector.

A: Consider the figure: Find the component of form of a vector v.   The component form of a vector in…