Let U = ((1, 1, 0, 1), (0, 1, 2, 3), (2, 3, 2,−1)) and W = ((1, 3, 4, 4), (1, 1, 0, 2)) be sub- spaces of R¹. (a) Find dim(U+W). (b) Compute dim(UnW). Justify your answer.

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

A:

Q: Find the transitive closure of R={(0,1),(0,2),(1,1), (1,3),(2,2),(3,0)}

A: Given relation is                              R=(0, 1), (0, 2), (1, 1), (1, 3), (2, 2), (3, 0) we…

Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Consider the points + (xo, yo) (x1, y₁) (x2, 12) (X3, 13) (X4, Y4) = = (-3,-4), (-1, 1), (0, 1), X =…

A: x -3 -1 0 2 3 y -4 1 1 5 9

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: Show whether the set {(2, –1, 3), (0, 3, 1), (- 1,1, -2)} in the space R³ is linearly independent.

A: Definition. Let V be a vector space. Vectors v1, v2, . . . ,vk ∈ V are  called linearly dependent if…

Q: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: (b) Let v₁ = (-2, 1,5), v₂ = (0, 1,4), V3 = (-2,4, 17). What is span(V1, V2, V3)? Could it be all of…

A: Given vectors are v1=(-2,2,5), v2=(0,1,4),v3=(-2,4,17) we have to find span(v1,v2,v3)

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

Q: line through the variable point A(k+1,2k) meets the lines 7x+y-16=0 ,5x-y-8=0,x-5y+8=0 at…

A:

Q: The distance from (-3,-4,-7) to the yz-plane is (A) -4 (B) 4 (C) -3 (D) 3 (E) 7

A: The distance(d) between two points (x1,y1,z1) and (x2,y2,z2) in a cartesian coordinate system is…

Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

A:

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

A:

Q: 7. Let u = (2,1, −1) and v = (√√2, 1, 1). Find the decomposition of u into vectors that are parallel…

A:

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Determine whether u, v and w lie in the same plane when positioned so that their initial points…

A:

Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

A:

Q: definition set and drawan the plane Find the

A: Using elementary properties of logarithmic function and square root function set is obtained then…

Q: Let u=<-1,1> v=<-3,4> and w=<0,-2> Find u-v+4w

A: