3. Suppose that {v1, v2, V3} is a basis for V and p:(v;) = dij. Let %3D W1 = 2v1 + v2, W2 = v1 - 2v3, W3 = 2v1 - V2 + V3, T = P1 8 41 ® P3. Calculate Alt T(w1,W2, W3). and %3D %3D

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Find a base for the line space of the matrix and determine the line rank.

A:

Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

A:

Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

A:

Q: Create a world transform matrix that translates by 3, 5, 7 and rotates 80° about the x-axis.

A: Detailed explanation mentioned below

Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

A:

Q: Define the term Change of basis?

A:

Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: a. Write the solution set to the following equation in parametric vector form (consider ₁ to be the…

A:

Q: The matrix that projects onto the x-y plane is

A: We have to find the matrix that project onto  plane

Q: Is A = diagonalizable. Justify your conclusion. 10 120 -3 5 2,

A:

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

A:

Q: Find the length of the projection of 3   onto the vector -3…

A:

Q: The vector x is in a subspace H with a basis ß = {b₁,b₂}. Find the ß-coordinate vector of x. b₁ =…

A: The given basis is b1,b2=1-2, -53. To Find: beta coordinate vector of x=19-17 w.r.t the above basis.

Q: Q4) Determine whether the set S is linearly independent or linearly dependent a) S = {(2,1,–2),…

A:

Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

A:

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

A:

Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

Q: Consider the set of vectors B = {(1, 0, 2), (2, 1, -1), (3, 0, 7)} (1) Is 3 linearly independent?…

A:

Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

A:

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.