3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1 (3) U: U2 · U3 1 4 1 V = 1 , V3 = 1 Vi = , V2 = -2 (a) For x = 3 u1+2 u2 – 4 u3, find the coordinate vector [x]u of x with respect to the U basis. (b) For the same x above, find the coordinate vector [x]y of x with respect to the V basis.

Q: Given vector u = (3, 1) and v (1,3) , determine the value of 2u – 3v in component form.

A: Use component wise addition and multiplication for required answer.

Q: Let B=[u, be a base for V=R², where = (1,2) and =(-1,1). We know that every vector in V is a linear…

A:

Q: 米 S = {u1, u2} for R2. 12. Find the coordinate vector of w relative to the basis %3D (a) u = (1,…

A:

Q: Find the coordinate vector of A relative to the basis S = {A1,A2‚A3,A4}. 3 4 A1 ,A2 ,A3 = ,A4 = ;A =…

A: The given vectors, S=A1, A2, A3, A4A1=1010, A2=1100, A3=1001, A4=0001; A=3436

Q: II. Determine whether or not the following sets of vectors {u , v , w} are both orthogonal and…

A:

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

A:

Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

A:

Q: w is the orthogonal projection of the vector v upon the vector u where v:=vector([1,-1,1]);…

A: The orthogonal complement If w is the orthogonal projection of the vector v upon the vector u is .

Q: Find the vector x determined by the given coordinate vector [x]B and the given basis B. -3 21) B =…

A:

Q: Let B, D be the following two bases of R°: 2 -1 B = 2 4 D = -3 -3 a) Find the change of coordinates…

A: Given: B=222, -122, -320 and D=4-3-1, 0-3-4, 1-2-2  To find: Change of coordinate matrix PD←B from…

Q: Let A = 5.7 ag -2.5ẩn and B = -1 âg+ 4an given the unit vectors = 0.6a+ 0.8ẩy and ẩh = 0.8ất – 0.6a…

A:

Q: Find the coordinate vector (x]g of x relative to the given basis B= (b1, b2, b3}. 5 b1 , b = 5 b3 =…

A:

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find the coordinate vector of = -1 with respect to the basis B = for IR3. 2 B

A:

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Let B = {b₁,b2, b3} be a basis of R³ where -0-8-0 b₂ = -4 b3 -3 b₁ = 2 5 Let V= - 5 Find the vector…

A:

Q: Find the new coordinate vector for the vector x after performing the specified change of basis.…

A:

Q: Find the vector z, given that u = , v = , and w = . z = 8u − 2v − 1/2w

A:

Q: 1. Show whether the following vectors are linearly independent or dependent. [1] [0] V1 = |2],v2 =…

A: We need to show the linear dependence or independence of the vectors which ever is applicable.…

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.