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Solve the system using Gaussian elimination or Gauss-Jordan elimination. -3x-3y-3z = 30 9x- 9y- 9z -90 -1.5x-1.5y-1.5z-15 Select one: a. (2, 2, 6)) Ob. {(x,y,z)1-3x-3y-3z = 30) Ос. { } Solve the system using Gaussian elimination or Gauss-Jordan elimination. -3x-3y-3z = 30 9x- 9y- 9z -90 -1.5x-1.5y-1.5z-15 Select one: a. (2, 2, 6)) Ob. {(x,y,z)1-3x-3y-3z = 30) Ос. { }
Please solve all questions 1. Let 0 : Z/9Z+Z/12Z be the map 6(x + 9Z) = 4.+ 12Z (a) Prove that o is a ring homomorphism. Note: You must first show that o is well-defined (b) Is o injective? explain (c) Is o surjective? explain 2. In Z, let I = (3) and J = (18). Show that the group I/J is isomorphic to the group Z6 but that the ring I/J is not ring-isomorphic to the ring Z6. 3....
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
7. Find the QR factorization of 3 6 -37 A = 14 8 6 0 4 5
Find the 44th percentile, P44, from the following data 3 5 17 37 19 38 20 24 6 27 62 85 40 74 80 46 83 92 94 81 95 P44
Market for Product O $24 $21 $18 $15 $12 $9 $6 $3 $0 0 6 12 18 24 30 36 42 48 54 60 66 72 78 In equilibrium, total surplus is (Select] If there is an increase in supply we know that consumer surplus [Select] If the government places a $9 tax on sellers then sellers receive (Select] If the government places a $9 tax on sellers then tax revenue will be (Select] If the government places a price...
h 7. Let A = 134 -1 2 6 6 0 6 3 9 0 9 2 -3 -3 0 Find basis for Nul(A) and Col(A). 3 و 3
b--27-3K the two following vectors+37-7 and B-27-3R a+37-4j and Determine the scalar product between the two following vectors 0 -18 0 +18 0
Verify the identity. (3 cos 0-6 sin 0)2 + (6 cos 0+3 sin 0)2 = 45 Choose the sequence of steps below that verifies the identity. O A. (3 cos 0-6 sin 0)2 + (6 cos 0 + 3 sin 0)2 = 9 cos - 36 sin 20 + 36 cos 20+9 sin ?e =9 (cos?0+ sin 20) +36 (cos 20+ sin ?e) = 9+ 36 = 45 O B. (3 cos 0 - 6 sin 0)2 + (6 cos...
y In 8 and 9, write a rule and an equation that represents the pattern in each table. Multi 1 2 3 4 5 33 34 35 36 37 mo 1 2 3 4 n 0 3 6 9 12 and 11, write a rule and an equation that represents the tn in each table. Then complete the table. g 32 37 42 47 52 09 18 27 36