5. Consider the basis aj = (1, 2, 3), az = (2, 4, 5), and az = (3, 5, 6) for R] × 3. Consider t E L(R] × 3, R] × 3). If 3 Mtx, „(r) = find Mtx, (7).

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

Q: Question 5: If a = ~q and KB = (p (q v r) ^~p, prove using the analysis method (proof based on…

A: We know

Q: Draw the Venn diagram with the following information: ANBNC={√2, √-1}, (ANB) NC'={2%, 00}),…

A: Here we eight disjoint parts , putting into them we can construct ven diagram

Q: If A = (a, b) and B= (b, c), find: (i) (AUB) (ii) (AnB)' (ii) A'UB

A:

Q: 3. If A = {1, 2} and B = {x, y}, then AXB = O {1,x), (1,y), (2,x), (2,y)} O {1,x), (2.y)} none of…

A: We have to solve given problem:

Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

A: We will solve the following

Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: Find the projection of u = onto v = .

A:

Q: 2] -1 1] a. Find SVD from A 1. A = [4 | b. Find SVD from A invers 2. A = [; : : 8] 1 0 0 0 a. Find…

A:

Q: Verify that the polynomials 2 – x², x' – x, 2 – 3x² and 3 – x' form a basis for P3(x). Express cach…

A:

Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Given that

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

A:

Q: If u=(1,4)�=(1,4)  and v=(3,2)�=(3,2)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

A:

Q: REMOVE vectors from Ac (P,[R], +,). To obtain a BASE for (P.[R],+,): of the items 25 and 26 (Item…

A:

Q: If a-(1/a)=b, b-(1/b)=c, c-(1/c)=a then abc=?

A: Given  a-1a=b....(1) b-1b=c....(2) c-1c=a....(3) We have to find abc

Q: Pargilelogram ABCD With Al-4,-3) BL-1, 4),C(5,66), D(2,-1) transiafe according to the roe (xiy)->(x…

A:

Q: 6. -4 Új = -5 U2 = 3 form a basis for R’ if and only if k #

A: Three vectors form the basis of ℝ3 if and only if the determinant of the matrix formed by the…

Q: 22. Find a basis for R4 that contains the vectors (3, 2, 3, 3) and (5, 4, 5, 5)

A:

Q: 6. Suppose that u₁ and u₂ are vectors with ||u₁||| = 2 and ||u₂|| = 3. You are also given that u₁ ·…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: If 1 A = -9 6 1 6. 2 -T and Q(#) = ' Až, then Q(z1, 12, T3) = Enter z1 as x1, 12 as x2, and 13 as…

A:

Q: Consider the DFA M = ({q0, q1, q2, 93}, {0, 1}, 8, go, {41, q2}), where d is defined as follows.…

A:

Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

A:

Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

Q: 9. Determine whether the set of vectors i (2,-1), (3,-2), (0, 1)} basis for TR? is

A: We will check whether the given set of vectors is a basis of R2 or not.

Q: Q3)) Let (Z8, +8) and H=(0,2,4, 6} .Find the normalizer of (H, +8) in (Z8, +8).

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 30²) For A = {• t, 1} & B = {₁, 0, 83 & universum U= {0, oto, 1, 0, 7, 3 Find: A', B', AUB, AnB, AB,…

A: (i) Consider the universal set is U=∘,+,1,⋄,7,Ω, A=∘,+,1 and B=1,⋄,Ω. (ii) Given U=ℝ×ℝ=ℝ2, A=x,y|x≥1…

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.