Number 4 part a b c d and e 13. Is 3x² in Span(x?14. Is sin(x +I|4)n Spanl3. Determine which of the following sets of functionsare subspaces of F[a, b].a) All functions f in F[a, b] for which f (a) = 0b) All functions f in F[a, b] for which f (a) = 1c) All functions f in C[a, b] for whichSa f(x) dx = 0d) All functions f in D[a, b] for whichf'(x) = f(x)e) All functions f in D[a, b] for which f'(x) = e*15. Determine if16. Determine if%3D4. Determine which of the following sets of n x n ma-trices are subspaces of Mnxn (R).17. Determine ifa) The n x n diagonal matricesb) The n x n upper triangular matricesc) The n x n symmetric matricesd) The n x n matrices of determinant zero18. Determine if0 1e) The n x n invertible matrices-1 05. If A is an m x n matrix and B is a nonzero elementof Rm, do the solutions to the system AX = B forma subspace of R"? Why or why not?19. Determine if x² - 1,20. Determine if x'+x,:6. Complex numbers a +bi where a and b are integersare called Gaussian integers. Do the Gaussian inte-gers form a subspace of the vector space of complexnumbers? Why or why not?Use the system of linear ecMaple or another appropricises 21-24.1. Do the sequences that converge to zero form a sub-space of the vector space of convergent sequences?How about the sequences that converge to a rationalnumber?121. Determine if-18. Do the series that converge to a positive number forma subspace of the vector space of convergent series?How about the series that converge absolutely?4-19. Isin Span-410. Isin Span 31[ -41 [ 2 1.

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Number 4 part a b c d and e 13. Is 3x² in Span(x?14. Is sin(x +I|4)n Spanl3. Determine which of the following sets of functionsare subspaces of F[a, b].a) All functions f in F[a, b] for which f (a) = 0b) All functions f in F[a, b] for which f (a) = 1c) All functions f in C[a, b] for whichSa f(x) dx = 0d) All functions f in D[a, b] for whichf'(x) = f(x)e) All functions f in D[a, b] for which f'(x) = e*15. Determine if16. Determine if%3D4. Determine which of the following sets of n x n ma-trices are subspaces of Mnxn (R).17. Determine ifa) The n x n diagonal matricesb) The n x n upper triangular matricesc) The n x n symmetric matricesd) The n x n matrices of determinant zero18. Determine if0 1e) The n x n invertible matrices-1 05. If A is an m x n matrix and B is a nonzero elementof Rm, do the solutions to the system AX = B forma subspace of R&#34;? Why or why not?19. Determine if x² - 1,20. Determine if x'+x,:6. Complex numbers a +bi where a and b are integersare called Gaussian integers. Do the Gaussian inte-gers form a subspace of the vector space of complexnumbers? Why or why not?Use the system of linear ecMaple or another appropricises 21-24.1. Do the sequences that converge to zero form a sub-space of the vector space of convergent sequences?How about the sequences that converge to a rationalnumber?121. Determine if-18. Do the series that converge to a positive number forma subspace of the vector space of convergent series?How about the series that converge absolutely?4-19. Isin Span-410. Isin Span 31[ -41 [ 2 1.

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4. Determine which of the following sets of n x n ma- trices are subspaces of Mnxn (R). a) The n x n diagonal matrices b) The n x n upper triangular matrices c) The n x n symmetric matrices d) The n x n matrices of determinant zero e) The n x n invertible matrices