(3) Consider the following LPP where a, b = R: maximize ax1 + bx2 subject to 4x1 + 3x2 ≥ 12 x1, x20 (a) Solve this LPP graphically. Hint: you should consider 4 cases which have to do with the possibile directions of the vector (a, b).
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- Find the set of values of 'a' if the points (1, 2) and (3, 4) lie to the same side of the straight line 3x -5y + a= 0.Find a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂Let a, b, and x denote vectors in R,,. (a) Simplify 3a + (5b -2a) + 2(b - a). (b) If 5x - a = 2(a + 2x),solve for x in terms of a.
- Find the equation y = FW passing through the points (-!g-21), (1,i5), (2,12) and (3,3)? Fined also y(0) ? ans: y (6)= 6,Q3/A/ If ā = i – 2j + k , b = i + 2j – 4k and c Find: i) (ā x b). (ā xc) ii) (ā x b) × (ā x c) Q3/B/ For what value of 2, the vectors 2i -j+ 2k and 3i + 21j are3 = [ ¹₂ ], b = [ ³ ], c = [ ¹₁ ], d = [¯^¹'], and v = [¯2²], 5. Given vectors a = (a) Find all real numbers x₁, x2, x3, x4, such that x₁a + x₂b + x3c + x4d = v (b) Write [at least] one sentence about what you have done above using the following mathematical term: linear combination. (c) Write [at least] one sentence about what you have done above using the following mathematical term: span.