3 Find a basis of the subspace of R’ defined by the equation -5x1 – 7x2 – 2x3 = 0.

Q: Find a basis of the subspace of R4 consisting of all vectors of the form. How can I even have an…

A: The vector x1-3x1+x2-5x1-5x2-5x1-3x2. We have to find the basis for this.

Q: 5. Show that if H and H2 are two orthogonal subspaces of H, then Hin H2 = {0}. Does the converse…

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Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

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Q: Find a basis for the subspace of R* spanned by S. s 3D {(2, 5, -3, -2), (-2, -3, 2, -3), (1, 3, —2,…

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Q: 2. Find the closest point to y in the subspace W spanned by vị and v2. 3 1 -2 y V2 13 3

A: To find  The closest point y in the subspace W spanned by v1 and v2.

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

A:

Q: Find a basis for the subspace of R" spanned by the following vectors. Го 3 -3 -2 -2 3 -3 -3 -2 6. -

A: NOTE: Refresh your page if you can't see any equations. . write all 4 given vectors in the matrix A

Q: Find a basis of the subspace of Rª defined by the equation 6x1 9x2 + 2x3 + 5x4 = 0 { Basis:

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 6

Q: Find a basis of the subspace of IR" defined by the equation 8ar1 - 7z2-4r3 0. { Basis:

A:

Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 2, 6), (-1, 3, 6), (2, 3, 1)}

A: The given subspace is: S= (1, 2, 6), (-1, 3, 6), (2, 3, 1)

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

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: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: Consider the subspace spanned by A ---- and 7₂ and the vector = basis {1, ₂}. = 5 9 in this…

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Q: Find the dimension of the subspace spanned by the given vectors.

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Q: Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

A: The given vector is y=-1-510 and the subspace is u=-200, v=12-1.

Q: Find a basis for the subspace given by the plane −3x + 2 y + 5z = 0.

A: Given that, -3x+2y+5z=0

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

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

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Q: Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R3 spanned by v1 = (1,…

A: See solution below

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

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Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: Let S be the set of all 2 × 2 real matrices given by   Find 2 × 2 matrices X, Y, Z such that S =…

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Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

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Q: 5 1 Find the orthogonal projection ŷ of the vector y onto the subspace W = Span { u = -7 3 Ex: 5 ||

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Q: Find a basis for the subspace of R3 spanned by S = {v1, v2, v3} = {(−1, 2, 5), (3, 0, 3), (5, 1,…

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Q: Next Find a basis of the subspace of R° spanned by the following vectors: -1 -5 3 -4 -4 -1 2 -4 3. 7…

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Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

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Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

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Q: Find a basis of the subspace of R* defined by the equation 2x1 + 9x2 + 4x3 + 9x4 = 0. %3D Basis:

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Q: 4) Find a basis for the subspace of R' spanned by the vectors. {(1,1,0,0), (0,0,1,1), (-2,0,2,2),…

A: We have fond the maximal linearly independent subset of the given set.

Q: Is the set of noninvertible 2 × 2 matrices a subspace of R2×2 ?

A: Given, ℝ2×2=abcd: a,b,c,d∈ℝ Let M be the set of all 2×2 noninvertible matrices  i.e.…

Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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Q: 2 2 , find the closest point to v in the subspace W spanned by 6 and 3 Given i = 6. 1 12

A: To find  The closest point to V in the subspace spaneed by the given vectors.

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: Find a basis of the subspace of R° defined by the equation 3x1 + 9x2 + 2x3 0. Basis:

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Q: Find the orthogonal projection ŷ of y = -5 onto the subspace 6. -2 W = Span { uį 4 3 u2 %3D -2 Ex:…

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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: Show that the set of vectors of the form a +b forms a subspace of R³. Find a 2а — b basis for this…

A: Given set of vectors of the form: aa+b2a-b Let v1=a1a1+b12a1-b1 and v2=a2a2+b22a2-b2 be two…

Q: The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for…

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Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the 1 2 2 - 1…

A: We have to solve given problem:

Q: Find a basis of the subspace of R defined by the equation 3x1 – 7x2 + 6x3 0. Basis:

A: Evaluation of basis problem.....

Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

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Q: determine whether the first vector is in the subspace of R3 generated by the other vectors. 1) (1,…

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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.