PROBLEMS
For Problems 1-14, determine the component
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Differential Equations and Linear Algebra (4th Edition)
- Find the angle between the vectors [ 1 ] And [ -3 ][ 3 ] [ 2 ][ 2 ] [ 5 ]arrow_forwardFor 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_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_forward
- If 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_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_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_forward
- Problems 3 and 4 refer to the vectors in the following diagram: b d 3. Which of the following statements is correct concerning the vectors in the diagram? (а) а—Ь%-с (b) d = 2b (c) d =a – 2b (d) c=d+b 4. The coordinates of a in the basis {b, c} are: (a) 3 (b) (c) (d)arrow_forwardA B -1 -2 C D E -4 -5 -3 F 1 GHI 2 3 L JK -1 -2 4 5 P Q R 2 3 1 MNO -5 -4 -3 TU S 4 5 -1 V -2 W X -3 -4 Y 1 N 2 Use the table above to create two vectors in 2-Space: * and y Let * be a vector representative of the first two letters in your given name and y represent the first two letters of your surname. (Ex. Albert Einstein: x= [-1, -2] and y = [-5,4]) My vectors are 2 = [-1₁-4] and j = [ -5, -2] Use the table above to create two vectors in 3-Space: è and f Let è be a vector representative of the first three letters in your given name and represent the first three letters of your surname. (Ex. Albert Einstein: € = [-1, -2, -2] and f = [-5,4,-4]) My vectors are è = [-1,-4, 2] and f= [-5, -2₁ -2] e 1. Angle Between Vectors and Projects a) Use the dot product to verify the type of angle connecting the vectors and y (acute, right or obtuse). b) Find the angle connecting the vectors and y in two different ways. c) Use the dot product to verify the type of angle connecting the vectors e and…arrow_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
- (3, 2), b = (4, –1), and c = =(8, 1). (a) Draw the vectors a =arrow_forward1. Let (1,2) and 7: = (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an 2. Consider the vectors (a) Is (b) Is = (3, a) be two vectors in R². Let = (1, 1, 1, 1) (1,2,3,0), = (0,1,2,3) and = (2,3,4,-3) a linear combination of a linear combination of are linearly independent? and ?? , and ?arrow_forwardIf v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forward
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