B = (v1, v2, V3) and B' = (w1, w2, w3) are bases of the vector space V. The change of basis matrix from B to B' is (1 2 4° Pg-→B = |1 2 3 2 3 5, If u = -v1 – 2v2 + 2v3 then [u]g a) b) c) 1 2 d) 6. 10 e) 14

Q: What is the scalar projection of vector a given by (a₁,a2,a3) in the direction of vector b given by…

A: We have to find the scalar projection of a in the direction of b.

Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

A:

Q: AB, BC, AC.

A:

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Answer considering the matrix with the given vectors as its columns

A:

Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: V is a vector space with bases B = (v1, V2, v3) and B' = (w1, w2, w3). The change of basis matrix 1…

A:

Q: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

A:

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

A:

Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

A:

Q: If vectors b, c and d are not coplanc then prove that vector

A:

Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: Find an orthogonal basis for A1, A2, A3 (i.e., find 3 mutually perpendicular vectors u1, u2, u3 with…

A: The solution are next step

Q: Express the vector in the form ai + bj + ck. 2) 8u - 5v if u = (1, 1, 0 ) and v = (3, 0, 1) A) v =…

A: u = <1,1,0> v= <3,0,1> We have to find 8u -5v

Q: Let i, j and k denote the standard basis vectors of R3 Let ü =i+ 25 –k and o = -i-+ 3k. a) Calculate…

A:

Q: Please don't provide handwritten solution ....

A:

Q: Find the terminal point Q of the vector v = 7i-j+3k given the initial point is P(-2, 3, 5) О (5, 2,…

A: In this question we have to find the terminal point of Q.

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

A:

Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

A:

Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: Given three linearly independent vectors V1 = (-1,4,-2,-4,-9), V2 = (-5,4,5,0,-4), Үз %3D (1,-3,9,…

A: The solution is given as

Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

A:

Q: B = (v1, v2, V3) and B' = (wi, w2, wz) are bases of a vector space V. The 1 1 2) change of basis…

A:

Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C,…

A: Given statements, (i) In triple dot of vectors (A×B)·C=(B×A)·C where the vectors A,B, and C are not…

Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: S= {(1,1,1), (1,2,-3), (5,-4,-1)} is a set in R'. Show that a) Sis orthogonal. b) Write w = (1, 5,…

A: Orthogonal set is the set in which dot product of two vectors is zero.

Q: Let V₁ = a) [¹ b) c). [3].2012 be 2 vectors in R². Show that S = {v₁, v2} is linearly independent.…

A:

Q: let az = (2,-1.0), az1 = (0,1,2), az2 = (1,-1,3) in R³ space. %3D %3D a) Can the vector (7,-6,7) be…

A:

Q: Construct an orthonormal set of vectors in ℝ3 from the set of linearly independent vectors ? =…

A:

Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 11.- Define the…

A: The given vectors .The aim is to find the norm of the vector .

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.