(4) Linear subspace L is given by the equations 2r1 + 12 + 3r3 - 14 3r1 + 2r2 – 2r4 3ri + 12 + 9r3 - 24 = 0 = 0 =0 Find equations describing the orthogonal complement L.

Q: 4. The set W of polynomials of the form a² + α₁x + α₂x² + 3x³ + α4x4, where a₁ = a₂ and a₁ = az is a…

A: 4. Given that the set W is of the polynomials a0+a1 x+a2 x2+a3 x3+a4 x4 where a0=a2 and a1=a3 is a…

Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

A: Let AX=0 213-1320-2319-1x1x2x3x4=000R2→R2-32R1 , R3→R3-32R1…

Q: The vector x is in a subspace H with a basis B = (b, ,b2). Find the B-coordinate vector of x. - 1 ,…

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Q: Question 3 X1+2x2 -2x1-4x2 :X1, X2 real numbers is a subspace of R3. Then dim H = %3D %3D 3x1+6x2

A: Given H=x1+2x2-2x1-4x23x1+6x2

Q: 1

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Q: The solutions of the equation 2x-y+z=0 define a subspace of dimension two in R3 called a plane that…

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Q: The solution space for this system is a subspace of Rº and so must be a line through the origin, a…

A: we have to find solution.

Q: Find the orthogonal projection of -10 14 11 V = 15 onto the subspace V of R4 spanned by -1 2 1 X1 =…

A:

Q: -5 6 Given v = 1 -8 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 1 5 and u4…

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Q: 2s 4s + 5t Let W be the set of all vectors of the form Show that W is a subspace of R* by finding…

A:

Q: §5.1, Exercise 17. For which scalars a, b, c do the solutions to the equation ax + by = c form a…

A: We have to find for which scalars a,b,c do the solutions to the equation ax+by=c from a  subspace of…

Q: a + 3b + 4d C+ d 14) Let H = :a, b, c, d in R -3a - 9b + 4c - 8d -C - d Find the dimension of the…

A: image is attached with detailed explnation

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. %3D 1…

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Q: 2. Find a nonzero vector that lies in the intersection of the plane {x + 2y + 3z = 0} 1 2 and the…

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Q: Find the dimension of the subspace spanned by the given vectors. - 1 - 7 4 3 2 - 1 - 10 7 ... The…

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Q: The solution space for this system is a subspace of R$ and so must be a line through the origin, a…

A:

Q: very vector of subspace W5 is orthogonal to each vector in subspace V5.

A:

Q: 7 Given v = -1 1 find the coordinates for v in the subspace W spanned by -1 4. U1 -2 and uz = -2 -2…

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Q: Show that the solution vectors of a consistent non-homogeneous system of m equations in n unknowns…

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Q: 1 for which x value span the vector subspace? -1 13 - 2 -1 O A) 2 в) .1 O C) 0 D) 1 O E) -2

A: We have to find x

Q: 4. The two parts of this question are unrelated. (a) Consider the set of matrices of the form where…

A:

Q: Find a basis of the subspace of R defined by the equation -7x1 – 5x2 – 4x3 = 0.

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Q: Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point…

A: Let, the point be (x,y,z) then the distance between (x,y,z) & (0,1,4) is:…

Q: Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero…

A:

Q: 4. The set W of polynomials of the form α₁ + α₁x + α₂x² + α3x³ + axª, where a = a₂ and a₁ = az is a…

A:

Q: -11 -3 1 2 Find the orthogonal projection of v = onto the subspace W spanned by 43 -5 -3 3 4 5 projw…

A: Given: v→=-11243-3 and W is a subspace spanned by -32-53, -3254, 12-35.

Q: The sequence B = (|1 3)) is a basis for the subspace U = {{ r2| |r1 – 3r2 + 2r3 = 0}. 13 The vector…

A: We have to find the coefficient for linear combination

Q: Question 9 Solve the problem. Let H = a + 3b + 4d c+d -3a-9b+ 4c - Sd -c-d Find the dimension of the…

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Q: a) Supppose H is a 2 dimensional subspace of R³ with a basis {b₁,b2}, and y is a vector given by b₁…

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Q: Find a basis of the subspace of R defined by the equation 6y, + 3y, – 4y, = 0 Basis:

A: Given data÷

Q: The solution space for this system is a subspace of R and so must be a line through the origin, a…

A:

Q: The vector x is in a subspace H with a basis ß= (b₁, b2]. Find the B-coordinate vector of x. -6-0-3…

A:

Q: -5 -2 -4 Given v = find the closest point to v in the subspace W spanned by -2 and 7 70

A: Let consider  v=−19−2−3, u1=−5−26−1, u2=−4−4770

Q: Write the complete solution as plus homogeneous solution which is the solution of Ax=0, remember…

A: This is a question of linear transformation. Represent the given system of equation in matrix form…

Q: 1 -1 -2 1 1 1 1 2 { -1 1 -2 2 -1 } 1 1 1 1 -1 2 -2 1 The dimension of the subspace spanned by the…

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Q: SOLVE FOR ORTHOGONALITY AND NORMALIZED CONDITION GIVEN THE 3 X 3 MATRIX. [1.000 1.000 1.000 0.686…

A: Given matrix is 1.0001.0001.0000.686-0.500-2.1860.314-0.5003.186

Q: (a) Every vector of R² is a linear combination of the vectors (-2,3), (1, 1) and (4,1)? (b) Is every…

A: This is a question of linear algebra.

Q: 4. The set W of polynomials of the form ao + α₁x + a₂x² + 3x³ + a₁x¹, where ao = a₂ and a₁ = a3 is a…

A: Set W is polynomial and W is subspace of P4. We find number of arbitrary constant in set W.

Q: 13 The set of solutions to the system of linear equations x1 – 2x2 + x3 = 0 2x1 - 3x2 + x3 = 0 is a…

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Q: Consider the system of equations on R² -x Y – 4x³ . 1. Find stable and unstable subspaces.

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Q: 5s 5s + 5t Let W be the set of all vectors of the form Show that W is a subspace of R* by finding…

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Q: (a) Find the matrix P describing the projection from R³ onto the subspace V = span{ 2 } 5. (b) Find…

A: The complete solutions are given below

Q: -15] 1 [2] Find the orthogonal projection of v: -11 onto the subspace V of IR spanned by and 0 -2…

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Q: Please see image

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Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: The cosine space F3 contains all combinations y(x) = A cos x+ B cos 2x+C cos 3x. Find a basis for…

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Q: Q19 Spanned The range of a matrix A equals the subspace spanned by its columns. True False

A: We have to check

Q: da basis of the subspace of IR* defined by the equation 5x1 + 9x2 + 8x3 + 6x4 = 0.

A: Explanation of the solution is given below...

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.