Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the equation ATx =0.

Q: Show that the equations x+ y +z = 4, 2x + 5y - 2z = 3, x + 7y - 7z = 5 are not consistent.

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Q: Find the general solution of thedifferential equation. (2+x)y'=3y

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Q: Explain how the direction vectors of two lines in ℝ3 can be used to determine whether the two lines…

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Q: Find two linearly independent solutions of 2r2y"- xy' + (-4x + 1)y = 0, x > 0 of the form Y1 = r (1+…

A: Given fill in the blanks have already some data, it is wrong as per given question. I solved it, and…

Q: What must be value of X so that B is diagonalizable?

A: A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: Find two linearly independent solutions to x2y′′+x(3−2x)y′+(1−2x)y =0 on (0,∞).

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Q: ?  kilogram child, ? meter(s)

A: Given that, two children weighting 15 and 22 kilograms are sitting on opposite sides of a seesaw,…

Q: If a vector gets multiplied by a positive number, its direction will be *.reversed FO TO

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Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

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Q: Choose a vector (b1, b2, b3) for which Ax = b can be solved, and another vector b that allows no…

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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: Write down the general solution of Ax = b in parametric vector form.

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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: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: 23. (f + 1)dv/dt + 2tv =-1

A: Let's find.

Q: Solve for the orthogonal traectories y2= 4x²(1- kx) %3D

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Q: At the point AI 2.4) was rotated counterclockwise A. LTS image would be located at 13 A'L 4-2) (21…

A: Let us take a random point x,y. If x,y is rotated counterclockwise by 90°, then the co-ordinates of…

Q: Based on the graph, give an example of linear combination that will result in a zero vector (weights…

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Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: We need to put the sign of absolute .value for every scalar or vector TRUE O FALSE O

A: THE STATEMENT IS FALSE  AS THE ABSOLUTE VALUE MEANS ONLY THE NUMERIC VALUE AND DOES NOT INCLUDE THE…

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: Solve the following simultaneous equations Using Cramer's rule. Show complete solution. 10x + 15y -…

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Q: Find the solution for the equations using Gauss-Jordan. Then ONLY give the answer for x+ y+x…

A: Given: x+y+2z=92x+4y−3z=13x+6y−5z=0

Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: If a vector gets multiplied by a positive number, its direction will be .reversed F TO

A: To check: Whether the statement “if a vector gets multiplied a positive number its direction will be…

Q: give vector form for the solution

A: Here we have to find the vector form

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: Two vectors ñ and m are said to be parallel if ñ-m-0

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Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: Replace the Cartesian equation with equivalentpolar equations. xy = 2

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: 14. dQ/dt + (2/10 + 2t)Q = 4 2(5 + t)² + C 5+t

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Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: Suppose column 5 of U has no pivot. Then x5 is a __ variable. The zero vector (is) (is not) the only…

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Q: Obtain the homogeneous linear equation satisfied by the following function.

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

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Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: Differentiate the following linear and non-linear equations, and give a reason that why its near or…

A: Disclaimer: Since you have posted a question with multiple questions, we will solve the first three…

Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: = -y² + 2x²y + 2x – xª, y1 = x² %3D

A: The Riccati equation is of the form

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…