1. Find all r E Z satisfying each of the following equations. (a) 3r = 2 (mod 7) (d) 9r = 3 (mod 5) (b) 5x +1 = 13 (mod 23) (c) 5x +1 = 13 (mod 26) (e) 5x = 1 (mod 6) (f) 3r =1 (mod 6)

Q: s9-3x then y If y O 89-3x)4 25 O 819-3x)4 25 O 8(0-3x)4 O -24(9-3x)4 O 24(9-3x)4

A: The function is given by,

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: et x, y E Z. We have (x+y)³ = (x+y)² (x+y) = (x² +2xy+y?)(x+y) = (x³+3x?y+3xy² + y³) = x³ + y3 od 3.

A:

Q: 16) If v = 9i + 3j, what is || 8v ||?

A: Recall: If v→ =v1i +v2j then , v→ =v12+v22

Q: 0.78125ab²1 9 112, 15 ² q. (3/8c²d¹²e" 2 -2 S. (6; ²K³) ²x 20K 1³ X 3₁1-3 (3) = P. (4a² b ²) ²³² × 3…

A: According to guideline given to us, in multiple question we are only allowed to answer only first…

Q: 7. I) Find, if possible, AB ond BA A= 3212/ 2.

A:

Q: Prove that 5n²+3n+2 € O(n²).

A:

Q: 18) If a and b are negative and c is positive, determine whether the following are positive or…

A:

Q: Find x and y 24 -2 22 [2x-2y 2 -2 20 21 o -10: [4 : 25 24y 25 2x+y -4

A: Given:

Q: Solve the systems of linear congruence equations.

A:

Q: 1. Let -1 3 [1 2 3] A = 2 1 4 [1 2 3] 0 1 2 -4 1 and C 2 1 -3 Find the following: (a) 24 (b) 2АB (c)…

A: Solve by matrix operations

Q: 6 4 3 5 9 7 10 ^ - :: ³ - 1 - - [H] A = 1 3 C B 6 4 2 0 8 11 5 2 if D=C-A, then the element d13 is:…

A:

Q: 2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if…

A: