Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a matrix whose Nullspace is span

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: Find a linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

A: A linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

Q: What is the relationship between a matrix and the i-hat and j-hat vectors

A: matrix is used to find the cross product of two vectors detailed solution is given below

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: Let u1 = (-1,1,3), u2 = (2, 1, –3), uz = (3,0, 1) are three vectors. %3D Find expansion of the…

A: We have to write in linear combination form

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: 7. Find a 2 x 2 matrix that reflects vectors in the (x, y) plane across the x axis. 8. Find a 2× 2…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Consider the given figure with the following conditions:

Q: A vector is rotated about the Y-axis 45 degrees and is subsequently rotated about the fixed X-axis…

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Q: Find the stable vector of 1 2 1 3 2 3

A: ANSWER:

Q: what is the smallest subspace containing the vectors u, v and w? what is the span of a set of…

A: Span is the all possible linear combination

Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: The vectors (2, 2, -1) and ( -1, 2, 2) are orthogonal. Divide them by their lengths to find…

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Q: Find a vector in 3d space whose magnitude is 4 and whose components have the largest possible sum

A: Find a vector in 3D space whose magnitude is 4 and whose components have the largest possible sum.…

Q: Find the standard matrix of the linear operator M : R → R³ that first rotates all vectors…

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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 vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Find the matrix of the orthogonal projection of R² onto ar + by 0. %3D

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

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Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-<u2,…

Q: orthonormal

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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: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

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: stable

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Q: Compute the standard matrix of the linear operator M : R³ → R° that first reflects all vectors about…

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Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: What helps to set of vectors linearly independent?

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Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

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: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

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Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Q: Find the rotation matrix that could be used to rotate the vector by –20° about the origin. Take…

A: Here we have to find the rotation matrix that could be used to rotate the vector [1  1]' by -20°…

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: How many matrices are there in the vector space Mmxn(Z2)?

A: The given vector space is Mm×nZ2.

Q: Find the stable vector of

A: Given information: In the given Markov model, there are 2 states. A state transition matrix consists…

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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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