PROBLEMS
For Problems 1-14, determine the component
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Differential Equations and Linear Algebra (4th Edition)
- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardIf v is any vector and n is any unit vector: (a) Show that v can be expressed as v = (v · â) Â+ĥ×(v x î) where the two terms represent components that are parallel and perpendicular to ôn, respectively. (b) Write the equation given above in (a) in index notation.arrow_forward(3, 2), b = (4, –1), and c = =(8, 1). (a) Draw the vectors a =arrow_forward
- If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forwardTwo vectors are given by d = (2.0 m)î - (5.0 m)ĵ + (1.0 mk !3! and 6 =(-1.0 mî + (1.0 m)î + (5.5 m)k. In unit-vector notation, find the following. (a) d+6 = (b) a-6 = (c) a third vector č such that a -6+2 =0 m toarrow_forwarda, b, and c are vectors. Then the expression a×c+b×a is (a) Meaningless (b) A vector collinear with a (c) A vector orthogonal to aarrow_forward
- If a= 3/2 write the following vectors in column vector form: -3a = ( ) 1.5a = ( )arrow_forwardSuppose we wish to find the coordinate vector of w = 4 relative to the basis S = { } 1. What system of equations must be solved to find that vector? W1 W2 W1 W2 + 2. And what is (w)s = II IIarrow_forwardIf vector A = [4/1] and vector B = [-3/2] find A-Barrow_forward
- For the following problems, you need to provide a clear and detailed solution. Work Problem1 1 (a) [. - | Determine if the vectors 0 and| 1 span R³. -2 3 (b;. -- ] Can these three vectors form a basis for R'.arrow_forward(3) Let a = -1 and b = 1 be two vectors. What is a2 b2 - |a · b2 ?arrow_forwardGiven a the vector equation r(t)=(3+4t)i+(−2+3t)j+(−3+1t)kr(t)=(3+4t)i+(−2+3t)j+(−3+1t)k, rewrite this in terms of the symmetric equations for the line. (quotient involving x) (quotient involving y) = (quotient involving z) =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning