Let S = {[k 1 0],[1 k 1],[0 1 k]}. Deter- mine all the real values of k so that S is a linearly depen- dent set.

Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

Q: 1. Suppose we would like to define a function f : Q→ Z by the formula f(r) = a +b, where a, b € Z…

A:

Q: Let G1 = (A1, B1) and G2 = (A2, B2) be interval-valued fuzzy strong graphs. Then G1 is isomorphic to…

A: As per the question we have two interval-valued fuzzy strong graphs G1 = (A1, B1) and G2=(A2, B2).…

Q: For a,bEN define the relation a -b if and only if ab is a perfect square. Is this relation…

A:

Q: Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра,…

A:

Q: The set {(1,2),(-2,4),(0,5)} is linearly dependent. O True O False

A: Set of vectors is said to be linearly dependent is at least one vector of the set can be expressed…

Q: Find the null space for A. 12 0 [4] -3 -4 -1 6-6 9 A = null(A) = span 100

A: The given matrix is A=120-3-4-16-69 We have to find the null space of the given matrix.

Q: For an integer t, prove that gcd(2t + 1, 9t + 4) = 1.

A:

Q: Which of the following sets is linearly independent? * O M={(1,3,4),(1,2,5),(-1,0,-2)} O M={(1,1…

A:

Q: Show that the set { 159 is linearly independent

A:

Q: Let f = {(1,-1), (4,-2), (9,-3), (16,4)} and g = {(-1,-2), (-2, -4), (-3,-6), (4,8)}. Show that gof…

A:

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

A:

Q: 11. ( a) b) ) Consider the relation on A Determine if the relation is refl Determine if the relation…

A:

Q: Let A = {2, 3, 4, 5, 6}, B = {11, 12, 13, 14, 15} and define the relation R from A to B by aRb if…

A:

Q: Determine whether x = (0 2 0 1 1) is a vertex of X1+ 2x2 – x4 + x5 max X1,X2,X3,x4,X5ER 2 X1 + x2…

A: The set of solution of the given system is a convex set. The extreme point/ vertex is the point…

Q: Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}.…

A:

Q: Let A := {1,2, 3, 4} := B. (a) What is the cartesian product of A and B. (b) Find S := {(a, b)[; €…

A: Given A=1, 2, 3, 4B=1, 2, 3, 4 (a) We have to find the cartesian product of A and B.

Q: Which of the following sets spans R°? None of these {(-3,0,2)} O {(-3,0,2),(5,1,0),(0,1,1)}…

A: The solution is given as

Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: List all the ordered pairs in the relation R= {(a, b) | gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

A: