Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector orthogonal to W. - 1 1 - 2 y = u1 U2 3 %3D 1 - 1 The sum is y =y+z, where y = is in W andz= is orthogonal to W.

Q: 3 0 -6 and u3 = 1 . Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the…

A: We have u1 and u2 are orthogonal, we have to construct a non zero vector v that is orthogonal to…

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

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Q: Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and…

A: First we have to construct a 2x3 matrix of rank 1. then find the vector in the subspace (row space…

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A: Firstly we have to find,

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Write vas the sum of two vector components if v= 2i+jand w=3/- 2j. O-(-+)+(¹+) O )+(¹+)) O (+)+(+) O…

A: Write v as the sum of two vector components if v=2i+j and w=3i-2j.

Q: Find a vector v parallel to the intersection of the planes - (x + y + 3z) = 4 and 3y - 3x - z = 7.…

A: Step 1: Step 2: Step 3: Step 4:

Q: False/True: If vectors V1, V2, ..., Un span the subspace V, then every vector in V can be written as…

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Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

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Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=<1,0,1>Q=<2,1,0> The component form of a vector is the ordered pair that…

Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

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Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: 1 1. Let ui = u2 = 2 and u = U3 -5 Let Wi = Span{u, u2} and W2 Span{u3, u4}. %3D (a) Show that the…

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: Consider the three vectors V1 = (1,0,0, –1), v2 = (0, 1, 1, 0), V3 = (1, 1, 1, 1). Let W be the…

A: Given that W be a subspace of R4 spanned by the vectors. v1=(1,0,0,-1), v2=(0,1,1,0), v3=(1,1,1,1)…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Find the closest point to y in the subspace W spanned by v₁ y = 5 1 1 15 - 1 1 - -1 2 V2 - 3 1 0 2…

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Q: Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S…

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Q: Let W be the subspace spanned by u₁ and u2, and write y as the sum of a vector in W and a vector…

A: Let W be the Subspace Spanned by u1 and u2,Write y as the sum of a vector in W and a vector…

Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: If W₁ and W₂ are subspaces of V and dim W₁ (a) W₁ = W₂. (c) W₂ C W₁. dim W2, then (b) W₁ C W₂. (d)…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: 2. Consider the vectors v₁ = [1, 1, 1] and v2 = [1, 0, 0]. These two vectors define a 2-dimensional…

A: Let us find the projections.

Q: →→→ Let x, y, z be vectors such that x X X y x z →→ = a; y x ➜>> Z X X y = b and ° {(+5) x = -(-+)}…

A: It is given that x→=y→=z→=2 x→,y→,z→  makes angle of 600 with each other.x→×y→×z→=a →  ; y→×z→×x→=b→…

Q: Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w] -1 5 -4 -2 Then…

A:

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: 2. Describe the subspace of R³ (is it a line or a plane or R³?) spanned by (a) the two vectors (1,…

A: Given data:- v1, v2,v3 are vectors in R3.

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.