1) dot product of two vectors can be found by
so
so answer is -8
option d
2) by using given matrices ax+by=z can be written as
then matrix form for this is
augmented matrix for this is
convert this to row reduced echelon form , then last column gives result . on converting this becomes
so solution is a=-3 b=2
so answer is option a
3) equation for a plane passing through points , and is given by the following equation containing determinent .
using given 3 points equation becomes
now solve this
(x-1)[6-4] -(y-1)[-6-12]+(z-1)[2+6]=0
2(x-1)+18(y-1)+8(z-1)=0
2x+18y+8z= 28
divide both side by 2 to get
x+9y+4z=14
so answer is
x+9y+4z=14
option b
these are 3 seperate questions please answer abcd for each 5 31 and v= 2 3...
theres two seperate questions please answer both either abcd Let u = Jand v-{2} Display the vectors u, v, and u + v on the same axes. O - 10 10 x 10 x -10 -5 10 X u u v - 10 10 -10 -5 10 5 -10 Let u = Find 2u+v. O -5 S - 13
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either provide a proof showing the set is a subspace of R3, or provide a counterexample showing it is not a subspace: [9 marks] (i) S= {(x, y, z) ER3 : 4.0 + 9y + 8z = 0} (ii) S = {(x, y, z) E R3 : xy = 0} (b) Determine for which values of b ER, the set S = {(x, y, z)...
2 seperate questions the last picture is part of the second question ( multiple choice) Let A and B benxn invertible matrices, then det(B-1 AB) = 0 det(A) det(B) -det(A) (1 2-3 51 The augmented matrix for a system is given as, 0 1 4-6. Find the general solution or state that 0 0 0 0 there is no solution x=5-2y+32 y=-6-42 z is free x=17 y=-6 z=1 0 O X 17 [11] y -6 +1 -4. N 0
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
use linear algebra methods to solve only please 2. Find the value(s) of a (if they exist) for which the system of equations has: (a) No solution. (b) One unique solution. (c) Infinitely many solutions. x + y - z = 2 x + 2y + z = 3 2x + y - 4z = a
Please show step by step how they got (1-4+(9/2))k^2 = 1 on the last line. Find the points on the hyperboloid x2 - y2 + 2z2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6). Then f(x,y,z)= x2 - y² + 2z? fe(x,y,z) = 2x 1,(x,y,z) =-2y f:(x, y, z) = 42 Comment Step 3 of 5 A Then yf(x, y, z)=< 2x - 2y, 4z > Let (xo, Yo, 2.)...
a - e (a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...
please answer all of them!! Question 6 Perform the indicated row transformation and write the new matrix. Multiply the numbers in the first row by 5 and add the product to the second row. 010 3655] (1 612) O 5 30 60 1-5 6-5] Question 7 Solve for the given letter. Question 8 Write the augmented matrix for the system. -2x + 2y + 4z = -10 6x + 6y + 4z = 2 6x + 9y + 4z =...
3. Use x = A-17 (you must) to solve the following system. It is known that the system has unique solution 2.0 + y + z = 4 10.x - 2y + 2z = -1 6.x - 2y + 4z = 8 (Answer: x = -1/2, y = 3/2 and 2 = 7/2)
Homework 4: please use python to find the answers. 1. Let A= 1 2 3 4 4 6 7 8 9 (a) What is A(2,3) (b) What is AT ? (c) Does A-1 exist? If yes, what is the value? 2. Let 2x + 3y + 4z = 1 -y +2 = 2 4x + y - 2 3 (a) What is the coefficient matrix? (b) Rewrite the linear system in the matrix form AX = b where X =...