Basic Math question and answers for January 11, 2024
- Q Given v= -7i+ 5j and w=-i-j.a. Find projwv.b. Decompose v into two vectors v? and v?, where v? is parallel to w and v? is orthogonal to w.
- Q Compute the following by usingA =[2 -1 5] b=[1 0 -2 ] and v=[1] [3 4 1] [2 3 4] ...
- Q Let u = 3i+ 3j, v=3i-j, and w= -5j.Find the specified scalar or vector.5u (3v-4w)
- Q Find the first six terms of the sequence.a? = 4, a? = 5; for n ?3, a? = a? - 1 + a? - 2
- Q An urban community would like to show that the incidence of breast cancer is higher in their area than in a nearby rural area. (PCB levels were found to be...
- Q Let be the subspaceW={(x +y, y, 2x?y)x, y ? R}with usual inner product, determine an orthogonal basis of W, the orthogonal complement of W and the projection of the vector...
- Q A study concluded that following 7 simple health rules can extend a man's life by 11 years on the average and a woman's life by 7 years. These 7 rules...
- Q Construct a consistent, unstable multistep method of order 2, other thanYn = -4yn-1 + 5yn-2 +4hfn-1+2hfn-2.
- Q Given the vector u=(1, -3), find the magnitude and angle in which the vector points (measuredcounterclockwise from the positive x-axis, 0? ?< 2?)counterclockwise||?|| =?=
- Q 1. Given an equation of the second degree3x + 12xy + 8y - 30x - 52y + 23 = 0a. Use translation and rotation to transform the equations in thesimplest...
- Q Suppose V is finite-dimensional with dim V>0, and suppose W is infinite-dimensional. Prove that L (V, W) is infinite-dimensional.
- Q Find the rank and nullity of the given matrix: 1 0 1 -1 6 2 -1 5 -1 7-1 1 -4 ...
- Q Consider three vectors u, v and w has the following relations:(m - 4) u + (m - 3m + 2) v + (m - 3m 4) w = 0(A) (l...
- Q Determine the values of r for which v = 1 is in the span of S = 1 , 1 ...
- Q Assume the vector space is defined by the following: {(x,y,z) |y=x, z=2x|}Does the definition satisfy the vector space axioms for addition and scalar multiplication?
- Q Let A be a 4 x 4 diagonalizable matrix. Which of these are always true about A?(I) A is similar to a diagonalizable matrix.(II) All the eigenvalues of A are...
- Q Let f be: R?R given by f(x,y) = (y -x) (y 2x)Show that f has no local minimum at (0,0), but that every restriction flg for every line G?R through...
- Q (10%) Let T be the function that maps R into R such that T(?) = proj??, where ?= (1, 1). (a) Find T(x, y). (b) Find T(5, 0). (c) Prove...
- Q A man pushes a lawn mower with a force of 30 i exerted at an angle of 30 to the ground. Find the horizontal and vertical components of the force,...
- Q Please fill in the following table with yeso to indicate which of these decompositions are applicable for A and B: LU without permutation, QR, SAS-, QAQ?, and U?V??Decomposition ...
- Q Sally and Sammy are on a merry-go-round. Sally sits twice as far from the center as Sammy. Sammy's tangential velocity would be...A. the same as Sally'sB. 1/2 of the tangential...
- Q A comet has an orbital radius twice that of the earth. What is the period of the comet in years?
- Q Find the x- and y-intercepts.y = |x + 1|-5Select one:a. x-intercepts: (4, 0) and (-6, 0); y-intercept: (0, -5)b. x-intercept: (4, 0); y-intercept: (0, -4)c. x-intercepts: (4, 0) and (-6,...
- Q Convert the rectangular equation to a polar equation.x + y = 16The polar equation of x + y = 16 is
- Q Rewrite the Cartesian equation y = 2x as a polar equation.r(0) =
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