3. Suppose v1, V2, V3, V4, V5 is linearly independent in F°. Show that v1, v2, V3, V4, V5, W is linearly dependent if and only if w E span (v1, v2, V3, V4, V5).

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Suppose that v1,..., Um is linearly independent in V and wE V. Prove that dim span(v1 + w,..., Vm +…

A: Let u1,u2,⋯,un be a set of vectors in a vector space V. This set of vectors is said to be linearly…

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

A:

Q: Suppose T 2 L(V; W) and v1; v2; :::; vm is a list of vectors in V such that T v1; T v2; :::; T vm is…

A: given :-  T ∈ L(V, W) and v1.............vm is a list of vectors in V such that {Tv1............Tvm}…

Q: Suppose S = {r, u, d} is a set of linearly independent vectors. If x =r + 2u + 5d, determine whether…

A: S=r,u,d is a set of linearly independent vectorsx=r+2u+5dT=r,u,x

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

A:

Q: Show that if S={v,v2,V3} is linearly independent and v, is not in Span{S}, then {V,V2, V3, V43 IS…

A:

Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: Suppose uy, v2, Vm is linearly independent in V and w E V. Prove that dim span (v1 + w, vz + ,... "m…

A:

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: Let v1, v2, V3 R° and suppose {v1, v2, V3 } is a linearly dependent set. Let A = [v1 v2 v3] E R5×3.…

A:

Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

A:

Q: Suppose u1, ūz and ūz are linearly independent. Let īj = ủ1+ ủ2, 02 = ủ1 + ủ3 and ī3 = ū2 + 2ūz.…

A: Given: Let u1→,u2→,u3→ are linearly independant. Let v1,→=u1→+u2→,v2,→=u1→+u3→,v3→=u2→+2u3→

Q: For what values of h is v3 in span {v1, v½} and for what values of h is {vi, V2, V3} linearly…

A: Given vectors  V1=133 , V2=39-1, V3=-2-6h 1) V3=Span{ v1, v2} 2) V1,V2,V3 is linearly dependent.

Q: Determine whether the following sets are linearly dependent or linearlyindependent. (a) {(; )( )} .…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: Draw v = [ 4/1 ] and w = [ -2/2 ] and v+w and v-w in a single xy plane.

A:

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

A:

Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2+x+3x² + 4x³, p₂ =…

A: Let V be a vector space . let v1,v2.....vn ∈V are linearly independent iff c1a1+c2a2+...+cnan=0…

Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

A:

Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

Q: Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions…

A:

Q: Suppose that S = {v} is a linearly dependent set. What is v?

A:

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

A:

Q: Which of the following sets is linearly independent? -ex-y-5=x+C OM= {(1,3),(3,9),(-1,-3)) M=…

A:

Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

A:

Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

A:

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

A:

Q: a. Is S = {v1, V2, V3} linearly independent

A:

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

A:

Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

A:

Q: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

A:

Q: Determine whether the set {p1,p2,p3} is linearly independent in P2, where p1 = 2+x+3x^2 +4x^3, p2 =…

A:

Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

A:

Q: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

A:

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

A:

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C (A 3x - 5y = k (B 5x + Зу - k ©…

A:

Q: In Exercises 9 and 10, (a) for what values of h is v; in Span {V1, v2}, and (b) for what values of h…

A: Please see the below picture for detailed solution.

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

A:

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: O let )ارارا ره( - V Vz = (i) show linearly independent if that )اراواو 2 - V is set generated by…

A:

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: Show that {x, y} is linearly dependent if and only if x or y is a multiple of the other.

A: It is given that, x and y are two distinct non-zero vectors.

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: If f = ux+v-y, g=u²+vy+ w and O(f.g,h) ô(11,v, w) h= zu -v+ vw compute

A:

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.