If A and B are distinct points in 3-space then |AB| = -|BA||

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: 4:: what the Null Space of is T;: R3 R³( T,x= xx a) R, R (T = X.Q

A: As per guidelines, we will solve first three sub-question: We have to find the null space of  1.…

Q: 3.3 Let r1 and r2 be distinct points in the metric space (S, d). Verify that there are open balls S,…

A: 3.3 is also known as Hausdorff Property. d(x1, x2) > 0 for every x1 ≠ x2   (metric space…

Q: Determine whether the set {P₁, P2, P3} is linearly independent in P₂=1+2x+3x² + 4x³ and p3 P₂, where…

A: The solution follows as:

Q: Use the sub no spaces: T-2y = - %3D 3x + 2y

A: Given that: x-2y=-10           ........(1)3x+2y=-14      ..............(2)

Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: Points A, B, C, and D are coplanar. A, B, and C are the only three of these points that are…

A:

Q: snip

A: Here given P2 is the vector space of polynomial with degree less or equal to 2, Thus 1, x, x2 is…

Q: A is symmetric

A: In this question, we have to check the matrix A is symmetric or not.

Q: The projection of onto the line through zero and is a. (G) b. d. 0.

A:

Q: 26) If x, y, u, v are variables connected by the relations 1 1 x? =au? +bv2, y² =au² –bv² where a…

A: Given, x2=au12+bv12…1y2=au12-bv12…2 Equation 1+2 gives:…

Q: 2. Consider the finite projective Geometry satisfying the well-known axioms A1-A6 and having exactly…

A:

Q: 18. Prove that if A, B, and C are any three distinct, collinear points, then either A-B-C, A-C-B, or…

A: Given A, B and C be three points that are distinct and collinear. Distinct means A≠B≠C and collinear…

Q: Let A = -{ and C = 31 %3D %3D If C+X-1= AB then X =

A: We can find the value of X as below.

Q: 3 0 Determine whether the set S = 0. CEE is linearly independent %3D or linearly dependent. O…

A: Linearly independent

Q: 23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з…

A:

Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2 + x + 3x² + 4x³,…

A: Here, to check the elements of P2 are linearly independent or not. For that, let…

Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

A:

Q: Find the null space for A. 1 8 A = -6 1 8 6 null(A) span

A: The given matrix is: A=  18-61   8 6

Q: - Show that the area of the triangle whose vertices are the [x1 yi det X2 Y2 A - points (x₁, y₁),…

A:

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

A:

Q: Suppose that two nondimensional quantities are exactly A chapter, express the four quantities (A+B),…

A: Given,          A=8.73       3 siginficant figuresB=1.389     4 siginficant figures

Q: Do the three planes x1 + 2x2 + x3 = 4, x2 – x3 = 1, and x1 + 3x2 = 0 have at least one common point…

A: The three planes x1+2x2+x3=4, x2-x3=1, and x1+3x2=0.

Q: Let r, y EN such that y # 0, then y+r#0.

A:

Q: 2 Let A B = -1 |0 and C = 7 Find x, y,z | 2 -3 such that AB =C.

A:

Q: Prove that X and Y are independent if and only if R = 0

A:

Q: Find the null space for A. 1 2 -2 1 0 1 3 A = null(A) = span

A:

Q: Determine whether or not T = (6,-3) belongs to the null space of A' if A 1

A: the answer is

Q: Let = (1,2). - a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) · ʊ = 0}. b. Draw the the…

A: v→=1,  2 S=(x, y) : x-3, y-1·v→=0

Q: 3.3 Let r1 and r2 be distinct points in the metric space (S, d). Verify that there are open balls S,…

A:

Q: 11. Let a, = 3 For what value(s) of h is b in the plane spanned h a =-8, b=-5 by a, and a2? %3D 2)

A: Given- a1=13-1 , a2=-5-82 , a3=3-5h To find value of h for which b in the plane is spanned by a1 and…

Q: Consider the set S of points in the complex plane defined by {i/n}, n 1, 2, 3, ... Discuss which of…

A: Solution: Here the set is S=in: n∈ℕ That is S=i1,i2,i3,...

Q: Theorem 2.6.9. If P and Q are two points such that P + Q, then there exists a point R such that P,…

A: Axioms used: 1. There is one and only one line that contains two distinct points. Given: Theorem…

Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

A:

Q: In the 2 dimensional space, which of the following points can not be represented as a convex…

A: We will find out the required values.

Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

Q: Show that and are not strictly convex.

A: To show that l1 and l∞ are not strictly convex.

Q: Determine whether the set {p1,p2,p3} is linearly independent in P2, where p1 = 2+x+3x^2 +4x^3, p2 =…

A:

Q: If A and B are distinct points in 3-space then |AB| = - Select one: True False

A:

Q: Show that; is a linearly independent set in R3.

A: S=121,011,201 Let a,b and c be the scalar in R3. Then write the set in term of linear span.…

Q: Solve the following inequality graphically in two-dimensional plane:y + 8 ≥ 2x

A: Given:

Q: 1. Is the following axiom system consistent/dependent? a. There are six points. b. There are three…

A: Given: The axiom system: (a.) There are six points. (b.) There are three 3-point lines. (c.) There…

Q: 18. Do the three planes x1 + 2x2 + x3 = 4, x2 – x3 = 1, and X1 + 3x2 = 0 have at least one common…

A:

Q: Theorem 8.11. For topological spaces X and Y, X ×Y is connected if and only if each of X and Y is…

A:

Q: Theorem 4P.1 There are exactly six lines in the four-point geometry.   proof the Theorem 4P.1 by…

A: To prove that in the Four point geometry , there are exactly six lines: the proof should be based on…

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

A:

Q: The set {t, –3t?} of P2 is linearly independent. O True O False

A: x=t  --------------equation 1y=-3t2  -------------equation 2now from equation 1 and 2y=-3x2means y…

Q: Show that X is Hausdorff if and only the diagonal A = {(x,x) | x € X} is closed in X x X.

A:

Q: Describe geometrically the set of points z satisfying the following condition:|z−2i|=3 .

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…