Let V be the set of all ordered pairs of real numbers under the following operations of addition 1. and scalar multiplication. Define addition and scalar multiplication on V as follows: (a, b) + (c,d) = (a + c −6, b + d + 1) and k(a, b) = (ka, kb) a. There exists a zero vector 0 in V such that for any v in V, 0 + v = v + 0 = v. Which ordered pair in V is the zero vector? b. V is not a vector space. Determine one of the vector space axioms that is not satisfied by V, and demonstrate with a counterexample.

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

A:

Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Let S be the set of matrices of the form a -a :). -b b where a and be R. The vector addition and…

A:

Q: Let Find a non-zero vector in the column space of A. A = -8 -8 12 -12 2 -2 -3 0 10 0 15

A: Solution

Q: a 12 Let A 0 a 1 For what value of a is A diagonalizable? Explain your 00 a answer.

A:

Q: Find the scalar triple product u (vxw). u. (vxw) = u = (-6,1,3), v = (3,6, - 8), w = (-4,3,2)

A:

Q: Let A be a 7 x 4 matrix and let v be a vector with 4 entries. Which of the following statements is…

A: as we know that when a matrix is multiplied by a vector then the product is a vector.

Q: Find the triple scalar product (u x v) w of u= 4i+ 2j- j, v=8i +5j- 4 k w= 5 i + 10 j - 9 k 102 29…

A:

Q: Let p (x) = ao + a¡x + a2x² and q (x) = bo + b1x + b2x² be vectors in P2 with inner product = aobo +…

A:

Q: Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector…

A:

Q: 1) the polynomial space p2 we consider the base (1+x 1+x² x+2x²) What is the coordinate vector of…

A:

Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

A:

Q: Compute the product using (a) the definition where Ax is the linear combination of the columns of A…

A:

Q: Show that u, v, and p are linearly independent-that is, none of the vectors is a linear combination…

A: To solve:α+2β=0 .....(i)4α−β=−9 .....(ii)−7α+4β=17 .....(iii)From the first two equations we…

Q: Let A = {1, 2, 3} and B = {1, 3, 5}. Let A × B denote the Cartesian product of A and B. Indicate if…

A:

Q: Given the set R² with the vector addition operation defined by (x₁₂1₁) (x₂, 1/₂) = (x₂+x₂₂3₁ +3₂ −2)…

A: Given a vector addition operation, we want to find the zero vector for the set .

Q: I have performed the following polynomial multiplication in matlab on two vectors of polynomial…

A: Since matlab is mymult=conv(v1, v2) and result is mymult=3 45 -6 -78 99 65 -54 -12 -10 240

Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

Q: Please solve this question with a good explanation. It is Linear Algebra question.

A:

Q: Let V be the set of all 2 × 3 matrices. Verify that V is a vector space.

A:

Q: {{: ]-- The set P = b = c = a + d } is a vector space under usual addition and multiplication. Find…

A:

Q: be the set of all vectors of the form 4r – 6s – 6t | r + 3s – 15t - 11r + 7s + 8t 14r + 11s 6t with…

A: We have to solve given problem: