5 32 CHAPTER 1 Linear Equations in Linear AlgebranortAworairt nowns of noitulos ePRACTICE PROBLEMS1. Prove that u + v = v +u for any u and v in R".omsiq Jam 2. For what value(s) of h will y be in Span{V₁, V2, V3} iffonsig5-4--------toloov oil noiioz on 2501.3 EXERCISES5. X₁dH65bas2. u = [2] . v = [-²]In Exercises 3 and 4, display the following vectors using arrowsamunon an xy-graph: u, v, -v, -2v, u + v, u-v, and u-2v. NoticeSTILL.COthat u - v is the vertex of a parallelogram whose other vertices areu, 0, and -v.01. u== [²1] = []mar 200 169nil bas asigillum als word 29. le olqmX₂ + 5x3 = 0³] manif brisnov.01613. u and v as in Exercise 1 4. u and v as in Exercise 2sachsvo no clcbus,nos no CS. lsdoténdated byIn Exercises 9 and 10, write a vector equation that is equivalent toIn Exercises 1 and 2, compute u + v and u-2v.anonsonqgA ni enol the given system of equations.HUB=+ x20-2va1.57. Vectors a, b, c, and d2010rol=*[3] + [3] + [6] - [8]6. X1x2x3-627pogolo Isrovni awobrisdilo alinu Imoves gniouborq to 1200 od among rb-V-UH=-50001 10100SUUse the accompanying figure to write each vector listed in Exer-cises 7 and 8 as a linear combination of u and v. Is every vector1in R2 a linear combination of u and v? TOY SVIO(bascovo bigod3. Let W1, W2, W3, u, and v be vectors in R". Suppose the vectors u and v are in Span{W1, W2, W3}. Show that u + v is also in Span (W₁, W2, W3}. [Hint: The solution toPractice Problem 3 requires the use of the definition of the span of a set of vectors.It is useful to review this definition on Page 30 before starting this exercise.]arTterü avrora dordynoitrupsUne comblIn Exercises 5 and 6, write a system of equations that is equivalent noo, oh Odoubring todizovacalato the given vector equation.ple), since1V CAXW2vVA=y-10110011²/Z 18V 1252falsinovi s to drownlo8. Vectors w, x, y, and zdolay sill204x1 + 6x2 - x3 = 0-x₁ + 3x₂ - 8x3 = 021 ling11. a₁ ==V3In Exercises 11 and 12, determine if b is a linear combination ofa1, a2, and a3.0, =------212. a₁ =1-214. A =-215. V₁ == bos= d2Geometric Desc In Exercises 13 and 14, determine if b is a linear combination ofwhichthe vectors formed from the columns of the matrix A.-113. A =tistimos-200810 dndFur=0, = 5 , =--------51 -4 20 3 5 ,b=1-2-63014 -2 5[1]-637016. V₁ =0uteng 2and y =10. 4x₁ + x2 + 3x3 = 9x₁ - 7x₂ - 2x3 = 28x₁ + 6x₂ - 5x3 = 1527.0²b3]-[-7, V₂ =, V2: =03-6211- -595303h88In Exercises 15 and 16, list five vectors in Span {V₁, V₂). For eachvector, show the weights on v₁ and v2 used to generate the vectorand list the three entries of the vector. Do not make a sketch., b =-1-[-²]6b= 1117

Question

5 32 CHAPTER 1 Linear Equations in Linear AlgebranortAworairt nowns of noitulos ePRACTICE PROBLEMS1. Prove that u + v = v +u for any u and v in R&#34;.omsiq Jam 2. For what value(s) of h will y be in Span{V₁, V2, V3} iffonsig5-4--------toloov oil noiioz on 2501.3 EXERCISES5. X₁dH65bas2. u = [2] . v = [-²]In Exercises 3 and 4, display the following vectors using arrowsamunon an xy-graph: u, v, -v, -2v, u + v, u-v, and u-2v. NoticeSTILL.COthat u - v is the vertex of a parallelogram whose other vertices areu, 0, and -v.01. u== [²1] = []mar 200 169nil bas asigillum als word 29. le olqmX₂ + 5x3 = 0³] manif brisnov.01613. u and v as in Exercise 1 4. u and v as in Exercise 2sachsvo no clcbus,nos no CS. lsdoténdated byIn Exercises 9 and 10, write a vector equation that is equivalent toIn Exercises 1 and 2, compute u + v and u-2v.anonsonqgA ni enol the given system of equations.HUB=+ x20-2va1.57. Vectors a, b, c, and d2010rol=*[3] + [3] + [6] - [8]6. X1x2x3-627pogolo Isrovni awobrisdilo alinu Imoves gniouborq to 1200 od among rb-V-UH=-50001 10100SUUse the accompanying figure to write each vector listed in Exer-cises 7 and 8 as a linear combination of u and v. Is every vector1in R2 a linear combination of u and v? TOY SVIO(bascovo bigod3. Let W1, W2, W3, u, and v be vectors in R&#34;. Suppose the vectors u and v are in Span{W1, W2, W3}. Show that u + v is also in Span (W₁, W2, W3}. [Hint: The solution toPractice Problem 3 requires the use of the definition of the span of a set of vectors.It is useful to review this definition on Page 30 before starting this exercise.]arTterü avrora dordynoitrupsUne comblIn Exercises 5 and 6, write a system of equations that is equivalent noo, oh Odoubring todizovacalato the given vector equation.ple), since1V CAXW2vVA=y-10110011²/Z 18V 1252falsinovi s to drownlo8. Vectors w, x, y, and zdolay sill204x1 + 6x2 - x3 = 0-x₁ + 3x₂ - 8x3 = 021 ling11. a₁ ==V3In Exercises 11 and 12, determine if b is a linear combination ofa1, a2, and a3.0, =------212. a₁ =1-214. A =-215. V₁ ==> bos= d2Geometric Desc In Exercises 13 and 14, determine if b is a linear combination ofwhichthe vectors formed from the columns of the matrix A.-113. A =tistimos-200810 dndFur=0, = 5 , =--------51 -4 20 3 5 ,b=1-2-63014 -2 5[1]-637016. V₁ =0uteng 2and y =10. 4x₁ + x2 + 3x3 = 9x₁ - 7x₂ - 2x3 = 28x₁ + 6x₂ - 5x3 = 1527.0²b3]-[-7, V₂ =, V2: =03-6211- -595303h88In Exercises 15 and 16, list five vectors in Span {V₁, V₂). For eachvector, show the weights on v₁ and v2 used to generate the vectorand list the three entries of the vector. Do not make a sketch., b =-1-[-²]6b= 1117

Accepted Answer

Answered: Image /qna-images/answer/3d43a62e-cf71-4338-87bc-1e24db28e34c.jpg

Ix F-CH+CH