PROBLEMS
For Problems 1-14, determine the component
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Differential Equations and Linear Algebra (4th Edition)
- a, 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_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_forward1. Write the vector H- 16 as a linear combination of the vectors and Darrow_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_forwardFind the angle between the vectors [ 1 ] And [ -3 ][ 3 ] [ 2 ][ 2 ] [ 5 ]arrow_forwardProblem #2: Let p = Problem #2: P₁ = 2x² + 6x + 9. Find the coordinate vector of p relative to the following basis for P2, 1 + x, P3 = 1+x+x². = 1, P2 Enter the coordinates, separated with commas.arrow_forward
- Problem #4: Let p = 7x² + 3x + 4. Find the coordinate vector of p relative to the following basis for P2, P₁ 1, P2 = 1 + x, P3 1+x+x². =arrow_forward[1 1 1 -1 Let u1 = u2 Uz = then write x as sum of two vectors -3 3 on in span {u} and other one in span {u2, U3,} -2 2 x = 3 -3 (a) X = (b) 3 2 0. 3 [1 (d) 1 X = 3 -3 4. + +arrow_forwardIf v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forward
- In a standard Cartesian coordinate system a vector, R, has an x-component of + 5.0 m and a y- component of - 4.0 meters. In the same coordinate system a vector F has an x-component of - 3.0 N and a y-component of 2.0 N. The cross product RxF is equal to 2.0 m*N in the + z direction 2.3 m*N in the - x direction 2.0 m*N in the - z direction 2.8 m*N in the + x direction 23 m*N in the - y directionarrow_forward[3] 1. Show whether the vector w = |1 is in span2 [5] 2. Show whether the following polynomial vectors are linearly independent or dependent. P1 = 1+ x, P2 = 1+ 2x², P3 = 2x + 3x²arrow_forwardThe following question is from linear algebra : Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step.arrow_forward
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