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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5 4bx- 2by = - 1
round each number to the nearest half 2 over 5
Find out the x-intercepts & y-intercepts for each of the following equations. y =x 2 +x - 6 Solution As verification for each of these we wil
Standard Basis Vectors The vector that is, i = (1, 0,0) is called a standard basis vector. In three dimensional (3D) space there are three standard basis vectors, i → = (1
Juan is g years old and Eva is 2 years younger than Juan. a.Find the sum of their ages in terms of g. b.Find the sum of their ages in g years'' time,in terms of g.
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
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To begin with we have counting numbers. These numbers are also known as natural numbers and are denoted by a symbol 'N'. These numbers are obtai
what is 10+10
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