Please help me solve these weekly practice questions. Please also provide the work, number and section.

The sections are :

From Additional Exercises ending Section 6.1:Exercises # 6.1.2 ; 6.1.3 ; 6.1.5 ; 6.1.6 ; 6.1.7

From Additional Exercises ending Section 6.2:Exercises # 6.2.2 ; 6.2.3

From Additional Exercises ending Section 6.3:Exercises # 6.3.2 ; 6.3.3

Student Home x Weekly Assignment 9 X zy 6.3. Coordinatiation X zy MATH 2000: Introduction to Line: X + X C @ learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/3?content_resource_id=44721378 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.3: Coordinatiation zyBooks catalog Help/FAQ Ibrahim Salam Feedback? CHALLENGE ACTIVITY 6.3.2: Change of coordinates matrices. Jump to level 1 Given the following bases for P2, find P , the change of coordinates matrix from B to C. C+B B = {2x2 - 2x - 10, -5x2 - 8x, -7x2 - 7x + 2} C = {a2 + +1, a+1,1} Ex: 5 P = CFB 2 3 4 5 Check Next Type here to search O XFOO 3:49 AM 10/17/2020Student Home x Weekly Assignment 9 X zy 6.3. Coordinatiation X zy MATH 2000: Introduction to Line: X + X C @ learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/3?content_resource_id=44721378 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.3: Coordinatiation zyBooks catalog ? Help/FAQ Ibrahim Salam Feedback? Exercise 6.3.2: Finding the coordinates of an element of a vector space with respect to a basis. About Find the coordinates of each element of a vector space with respect to the given basis. (a) V = (b) p(x) = 5+ 5x - 2x2, B = {1, 1 - x, 2 - 4x + 22 } of P2 (C ) Feedback? Exercise 6.3.3: Finding the change of coordinates matrix. About Find the change of coordinates matrix from basis 1 to basis C of the given vector space. (a) Bases B = Type here to search O SXFOO 3:49 AM 10/17/2020Student Home x Weekly Assignment 9 X zy 6.3. Coordinatiation X zy MATH 2000: Introduction to Line: X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/3?content_resource_id=44721378 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.3: Coordinatiation zyBooks catalog Help/FAQ Ibrahim Salam ( C ) Feedback? Exercise 6.3.3: Finding the change of coordinates matrix. About Find the change of coordinates matrix from basis 1 to basis C of the given vector space. (a) Bases B - 3 3] [ ])----{ . .323 (b) Bases B = {1, 1 + x, 1 + x + x2} and C = {1 + x2, x + 22, x } of P2 (c) Bases B = R2x2 Feedback? Exercise 6.3.4: Proving properties of coordinatiation. About Type here to search O XFOO 3:49 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.1. General vector spaces X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/1?content_resource_id=44721343 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.1: General vector spaces zyBooks catalog ? Help/FAQ Ibrahim Salam Feedback? Exercise 6.1.2: Understanding the field axioms. About Explain why each set is not a field. (a) The set of all invertible n X n matrices with real entries (b) The set of all complex numbers a + bi where a, be Z (c) The set of all nonnegative real numbers. (d) The set of all even integers 27 Feedback? Exercise 6.1.3: Proving that a set is a vector space. i About Prove that V is a vector space under the given operations. (a) V = R over R where addition is defined as a + y = cy and scalar multiplication is defined as c . a = a Type here to search O m 3:50 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.1. General vector spaces X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/1?content_resource_id=44721343 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.1: General vector spaces zyBooks catalog Help/FAQ Ibrahim Salam (c) The set of all nonnegative real numbers. (d) The set of all even integers 27 Feedback? Exercise 6.1.3: Proving that a set is a vector space. i About Prove that V is a vector space under the given operations. (a) V = R+ over R where addition is defined as a + y = cy and scalar multiplication is defined as c . a = a (b ) V = R2x2 under matrix addition and scalar multiplication Feedback? Exercise 6.1.4: Vector spaces. About Determine whether the statement is true or false. Justify each answer or provide a counterexample when appropriate. (a) If F is a field. then F is a vector space Type here to search O m XFOO 3:50 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.1. General vector spaces X + X C @ learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/1?content_resource_id=44721343 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.1: General vector spaces zyBooks catalog ? Help/FAQ Ibrahim Salam Feedback? Exercise 6.1.5: Basis and dimension. About Determine whether the statement is true or false. Justify each answer or provide a counterexample when appropriate. (a) The dimension of P3 is 3. (b) The dimension of 2x3 is 6. (c) An arbitrary element of a subspace W of a vector space has 2 free variables. Then a basis for W contains 2 elements. Feedback? Exercise 6.1.6: Determining whether a set is a basis for a vector space. i About Determine whether each set of polynomials in P2 form a basis. (a) {-ac + 1, 202 + 1} (b) {-2 + 1, x2 + 2, 202 - 2 + 2, 202 + 3 } Type here to search O XFOO 3:50 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.1. General vector spaces X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/1?content_resource_id=44721343 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.1: General vector spaces zyBooks catalog ? Help/FAQ Ibrahim Salam (c) An arbitrary element of a subspace W of a vector space has 2 free variables. Then a basis for W contains 2 elements. Feedback? Exercise 6.1.6: Determining whether a set is a basis for a vector space. About Determine whether each set of polynomials in P2 form a basis. (a) {-ac + 1, x2+1} (b) {-2 + 1, 202 + 20, 202 - 2 + 2, 202 + 3 } (C) {-202 + 1, -202 + 20, 202 - 220 + 2} (d) {-202 + 1, -202 - 2x + 3, -2x + 2, 202 - 2x + 2} Feedback? Exercise 6.1.7: Reducing a set to a basis for a vector space. About Type here to search O XFOO 3:50 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.1. General vector spaces X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/1?content_resource_id=44721343 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.1: General vector spaces zyBooks catalog Help/FAQ Ibrahim Salam (c) {-202 + 1, -202 + 20, 202 - 220 + 2} (d) {-202 + 1, -202 - 23 + 3, -220 + 2, 202 - 220+2} Feedback? Exercise 6.1.7: Reducing a set to a basis for a vector space. i About Reduce each set to a basis for the given vector space. (a) The set of polynomials {ac" + ac, a2 + ac + 1, 6ac2 + 3ac + 1, 2ac2 + 2ac + 1} in P2 (b) The set of matrices Box ? Feedback? How was this section? 1 1 Provide feedback 6.2 Subspaces Type here to search O 3:50 AM 10/17/2020Student Home x Weekly Assignment 9 x zy 6.3. Coordinatiation x zy MATH 2000: Introduction to Line: X zy 6.2. Subspaces X + X C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/2?content_resource_id=44721368 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.2: Subspaces zyBooks catalog Help/FAQ Ibrahim Salam (b ) Every subspace of a vector space is a vector space. Feedback? Exercise 6.2.2: Determining whether a subset of a vector space forms a subspace. About Determine whether each subset of a vector space forms a subspace. (a) The subset W of Pn that contains all polynomials of degree in or less that have all negative coefficients. (b) The subset W = R of R where addition is defined as a + y = ay and scalar multiplication is defined as c . a = a (c) The subset W of Rnxn for which the trace - the sum of the diagonal entries of a matrix - is zero. (d) The subset W of C[a, b] such that lim f(x) = M where a C a learn.zybooks.com/zybook/MACOMBMATH2000WensonFall2020/chapter/6/section/2?content_resource_id=44721368 =zyBooks My library > MATH 2000: Introduction to Linear Algebra home > 6.2: Subspaces zyBooks catalog Help/FAQ Ibrahim Salam (c) The subset W of Rnxn for which the trace - the sum of the diagonal entries of a matrix - is zero. (d) The subset W of C[a, b] such that lim f(x) = M where a