1. Suppose Vị , V2, V3, V4 spans V. Prove that the list Vị + v2 + V3 + V4, V2 + V3 + V4, V3 + V4, V4 also spans V.

Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

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Q: Show that projv u and u - projv u are orthogonal.

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Q: An architect designing a parking lot has a row 62.0 m wide to divide into spaces for compact cars…

A: We need to formulate a system of linear equations using the scenario. We also need to solve the…

Q: Find projvu.u = (−1, 3, 1), v = (4, 0, 5)

A:

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: 10 What is the preimage of (3, 5) under the translation (x, y) (x-4, y + 6)? O (7, -1) O (1, 1) O(1,…

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Q: • Let v = (-1,3). Draw v, -2v, and 3v in standard position. 10 10 -8 -6-4-2 2. -2 6. 8 10 -6 -8 -10…

A: solve

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

A:

Q: List all of the subsets of (x, y, z).

A: Given that the set x,y,z. Find all the subsets of the given set. Definition: A set is a well-defined…

Q: b) Show that z, + z, = z, + Z, . 2

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Q: Let ū (7, – 4, – 2) and i (6, – 1, 4). - - - Compute the following: v x ú = || и хиE 5(ū x i) = йх…

A:

Q: Let A, = {..., – 2,- 1,0,1,...,i}. Find

A: Ai={..., -2, -1, 0, 1, ......, i} ∩i=1nAi=?

Q: Prove that [2,5] and (3,4) have the same cardinality.

A:

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t…

A: To write the gcd(117, 213) as a linear combination.

Q: Prove that, there is no simple grcup of order 200.

A:

Q: Show that z, + z, = =, + 2 .

A: We have to prove that z1+z2=z1+z2 Conjugation: Let z=x+iy be a complex number. Then, the complex…

Q: Find projvu.u = (0, −1, 2), v = (3, 2, 4)

A:

Q: Determine whether the points are coplanar.(1, −5, 9), (−1, −5, 9), (1, −5, −9), (−1, −5, −9)

A:

Q: Let X = {a, b, c, d, e} and let T= {X, ø, {a}, {c,d}, {a,c,d}, {b,c,d,e}}, then * (X, T) is not…

A: Option 2 is correct.

Q: Let A, = {..., – 2, – 1,0,1,..., i}. Find ỦA, i31

A: First we find A1, A2, A3,...An, then find union as in next step.

Q: 4 A school has 137 math students. a) Prove that if the principal hires 8 math teachers, then at…

A: According to the given information, Number of math students in school = 137 For part (a) it is…

Q: 2. and as= Determine ifb=-1 =-2 is a linear combination ofaL az

A: Follow the procedure given below.

Q: Compute the orders of: U(5), U(7), U(35)

A: Note that, U(n) represents a group consisting of non-negative integers which are less than n and are…

Q: Suppose u=⟨−4,4,−2⟩ and v=⟨4,−2,3⟩. Then u×v=   v×u=

A:

Q: 13. Find the projection of (1,2, 3) onto (a, 3,7)

A: Here are two vectors are given and we have to find projection so use it

Q: If z,,z,€C then Zz=Z2 OZi+Z2=Z,+z2 OZi+z2=0 Z,Z2=0=Z,=0 or zz=0

A: 2nd and 4th options are correct.

Q: ) Suppose X = {1,2, 3} and Y = {5,6). The number of elements of the set P(X × Y) = %3D

A: Number of Elements in Power Set P(A) of set A with n elements is 2n

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В %3 {3, 1, 9, e, а, с, 0}, and C 3D {2, с, 10, 9, 8, —4,…

A: solution of the given problem is below...

Q: Determine if the set is linearly independent. S = {(4,0,1), (0, -3,2), (5,10,0)}

A:

Q: Suppose the universe U={1,2,3,4,5,6,7,8,9} and you have two subsets A={1,2,3,4} and B={2,4,6,8}Which…

A: Given the universe U={1,2,3,4,5,6,7,8,9} and the two subsets A={1,2,3,4} and B={2,4,6,8}

Q: Find projvu.u = (2, 5), v = (0, 5)

A:

Q: Determine whether or not the set {(2, 21, 0), (1, 2, 5), (7, 21, 5)} islinearly independent over R.

A:

Q: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

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Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

A:

Q: let u=(8,0,-8) v=(8,3,16) find Il v||

A: ||v||=√329

Q: find the complement of set B, given that U= {x ∈ z/ - 7 < x < 7}     A= {x ∈ z+ /2 < x < 6}     B=…

A:

Q: 4. Find a translation that maps A(2, –3) onto B(4,–2).

A: Given that: A(2, -3) and B(4, -2)

Q: 2. Show that if u is a SC

A: Given, if u is a solution of                          ∇2u+D(x, y)∂u∂x+E(x, y)∂u∂x=-F(x, y) in D with…

Q: Consider the partition P of [0, 1] be given by P = {0, 1/8, 1/4, 1/3, 2/3, 3/4, 1}. What is the norm…

A: Here given that the partition P of 0, 1 be given by P=0, 18, 14, 13, 23, 34, 1 .We have to find the…

Q: Find the norm of the partitionP={1,1.1,1.7,2.4,2.9,3.1,3.8,4}

A: Given Partition, To find the Norm of Partition.

Q: Find projvu.u = (2, −1), v = (7, 6)

A: Now dot product is,

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove &lt;-…

Q: If i and i are in R™, then –i is in span {ū, 3}. |

A:

Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: Find projvu.u = (2, 4), v = (1, −5)

A: The projection of u onto v is denoted as projvu. The following formula is used to find projvu.…

Q: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

Q: Which elements of the poset ({2,4,5,10,12,20,25}, |) are maximal, and which are minimal?

A: Draw the Hasse diagram to the given partially ordered set 2,4,5,10,12,20,25 by using the…

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

Q: If A subut of B. where B 18 a closo d subset of IR show that

A: Given: A is a subset of B, where B is closed subset of ℝp. To show: A¯⊆B.

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.