1) We know what a vector is, and we know how to measure the cosine similarity between two vectors using their dot products (it's the cosine of the angle between those vectors). Now let's start off our assignment with an easy one, let me give you a couple of vectors, A = WNI and B = What is the cosine similarity between A and B ? 2) i) Let u = (37) V = and w = (75). Then w can be written as a linear combination of u and v as follow: au + bv = w where a and b are real numbers. Write down the value of a and b? [12 3] 5-571 [C11 C12 C13] ii) Let A = 45 6 and B = - 2 4 Suppose BA = C21 C22 C23 . What is the value 785. C31 C32 C33] of C32? 3) Determine whether each of the following sets are linearly independent / dependent: (i) {(4 , -4, 8 , 0) , (2 , 2, 4, 0) , (6, 0, 0, 2), (6, 3,-3,0)}. (ii) (ii) {(1 , 3 , 2) , (1 , -7 , - 8) , (2, 1, - 1)} . 4) 2x + 5y + 5z = 0, - x - y = 0 and 2x + 4y + 3z = 0 are the three straight lines. These lines intersect each other at (1.7, -1.6). The inverse of a straight line is also a straight line. Find out the inverse straight line of these lines (Show all the steps) 5) a) Eliminate the following system by Gauss Jordan elimination X1 + 3x2 - 2x3 + 2x5 = 0 2x1 + 6x2- 5X3 - 2x4 + 4x5 -3x6 = -1 5x3 + 10x4 + 15x6 = 5 2x1 + 6x2 + 8X4 + 4x5 + 18x6 = 6