Find the coordinates of vector u=(4,5) with respect to linear basis ((2,1),(1,-1) ? a. 2 b. 3 • 2 O c. -2 d. -3 -1 N m m 2

Q: Determine and construct the vector c= a x b, where (1) a = 3 i and b = 2 k. (2) a = i +j and b = i…

A: To determine c=a×b 1 a=3i^, b=2k^2 a=i^+j^,  b=i^-j^3 a=2i^+3j^,  b=3j^+2k^

Q: Find the coordinate vector of w relative to the basis S = ({u₁. u₂) for R². u₁ = (4, - 4), u₂ = (2,…

A:

Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

A:

Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

A:

Q: Find the vector equation for the line passing through the points P₁(-3, 6, 8) and P₂(−6, 0, 12). 0 0…

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: Find a non-zero vector perpendicular to the vectors and ú =

A:

Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Find the coordinate vector of P relative to the basis S = {P1P2.P3} P1 = 1 +x+x*,P2 = x + x, p3 =…

A:

Q: (1 point) Express the vector = 8 as a sum of the basis vectors x = and y = %3D -13 xt j. = Netes V

A:

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: determine nonzero vectors that are orthogonal to the following vector (b).  (1, -2, 3) c. (5, 1, -1)

A: Let the vectors be- u→=xi^+yj^+zk^v→=i^-2j^+3k^ For the vectors to be orthogonal-…

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

A:

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: The plane passing through the three points A(0, 1,3), B(3,4,3) and C(2,3, –1) can be expressed as a…

A:

Q: Find the coordinate vector of v relative to the basis S = {v1, v2, V3} for R3. v = (-11,–17,7) V1 =…

A:

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , č = {0, – 1, 2} and (ii) ā =…

A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…