solve number 29 of the first picture using the second picture you are able to see the matrix which is problem #27 of the second picture. mogeneous linear system Ax = b, where A is a fixedm x n matrix and b ( 0) is a fixed vector.8. VR2, and S consists of all vectors (x, y) satisfyingx² - y² = 0.=9. V =M₂ (R), and S is the subset of all 2 × 2 matriceswith det(A) = 1.10. V = Mn (R), and S is the subset of all n x n lowertriangular matrices.11. V =Mn (R), and S is the subset of all n x n invertiblematrices.12. V M₂ (R), and S is the subset of all 2 × 2 matriceswhose four elements sum to zero.13. V = M3×2(R), and S is the subset of all 3 × 2matrices such that the elements in each column sumto zero.14. V M2x3 (R), and S is the subset of all 2 × 3 matricessuch that the elements in each row sum to 10.15. V =M₂ (R), and S is the subset of all 2 × 2 realsymmetric matrices.16. V is the vector space of all real-valued functions de-fined on the interval [a, b], and S is the subset of Vconsisting of all real-valued functions [a, b] satisfyingf(a) = 5. f(b).17. V is the vector space of all real-valued functions de-fined on the interval [a, b], and S is the subset of Vconsisting of all real-valued functions [a, b] satisfyingf(a) = 1.on I.For Problems 23-29, determine the null space of the givenmatrix A.23. A = [1 4].24. A =25. A:26. A==27. A:=28. A = =29. A =[1 −3 2].[32 -412-3 -5y" +2y-y=112345678−1[1-24 -7 -23ܨܚ ܡܐ ܀3-2310 -42 5-61i -24i -5-1 -3i i1630. Show that the set of all solutions to the nonhomoge-neous differential equation to the mnearx - 2yz = 0.Determine a set of vectors that spans S.24. Let S be the subspace of P3 (R) consisting of all poly-nomials p(x) in P3 (R) such that p'(x) = 0. Find a setof vectors that spans S.For Problems 25–33, determine a spanning set for the nullspace of the given matrix A.25. The matrix A defined in Problem 23 in Section 4.3.26. The matrix A defined in Problem 24 in Section 4.3.27. The matrix A defined in Problem 25 in Section 4.3.28. The matrix A defined in Problem 26 in Section 4.3.29. The matrix A defined in Problem 27 in Section 4.3.30. The matrix A defined in Problem 28 in Section 4.3.31. The matrix A defined in Problem 29 in Section 4.3.123 51 3 4 2246 -132. A =41. Consider the vectors01A₁ = [2 ~]-42= [-2 1] -4 = [19]A1A2A32in M₂ (R). Determine span{A₁, A2, A3}.42. Consider the vectors2 nes m spankP1, P2J.12^-[43]^2-[73]A2-1A₁ ==1 −1in M₂ (R). Find span{A1, A2}, and determine whetheror not Blies in this subspace.1[34]43. Let V = C(I) and let S be the subspace of Vspanned by the functionsf(x)=coshx, g(x) = sinhx.(a) Give an expression for a general vector in S.(b) Show that S is also spanned by the functionsh(x) = e*, j(x) = e¯x.

Question

solve number 29 of the first picture using the second picture you are able to see the matrix which is problem #27 of the second picture. mogeneous linear system Ax = b, where A is a fixedm x n matrix and b ( 0) is a fixed vector.8. VR2, and S consists of all vectors (x, y) satisfyingx² - y² = 0.=9. V =M₂ (R), and S is the subset of all 2 × 2 matriceswith det(A) = 1.10. V = Mn (R), and S is the subset of all n x n lowertriangular matrices.11. V =Mn (R), and S is the subset of all n x n invertiblematrices.12. V M₂ (R), and S is the subset of all 2 × 2 matriceswhose four elements sum to zero.13. V = M3×2(R), and S is the subset of all 3 × 2matrices such that the elements in each column sumto zero.14. V M2x3 (R), and S is the subset of all 2 × 3 matricessuch that the elements in each row sum to 10.15. V =M₂ (R), and S is the subset of all 2 × 2 realsymmetric matrices.16. V is the vector space of all real-valued functions de-fined on the interval [a, b], and S is the subset of Vconsisting of all real-valued functions [a, b] satisfyingf(a) = 5. f(b).17. V is the vector space of all real-valued functions de-fined on the interval [a, b], and S is the subset of Vconsisting of all real-valued functions [a, b] satisfyingf(a) = 1.on I.For Problems 23-29, determine the null space of the givenmatrix A.23. A = [1 4].24. A =25. A:26. A==27. A:=28. A = =29. A =[1 −3 2].[32 -412-3 -5y&#34; +2y-y=112345678−1[1-24 -7 -23ܨܚ ܡܐ ܀3-2310 -42 5-61i -24i -5-1 -3i i1630. Show that the set of all solutions to the nonhomoge-neous differential equation to the mnearx - 2yz = 0.Determine a set of vectors that spans S.24. Let S be the subspace of P3 (R) consisting of all poly-nomials p(x) in P3 (R) such that p'(x) = 0. Find a setof vectors that spans S.For Problems 25–33, determine a spanning set for the nullspace of the given matrix A.25. The matrix A defined in Problem 23 in Section 4.3.26. The matrix A defined in Problem 24 in Section 4.3.27. The matrix A defined in Problem 25 in Section 4.3.28. The matrix A defined in Problem 26 in Section 4.3.29. The matrix A defined in Problem 27 in Section 4.3.30. The matrix A defined in Problem 28 in Section 4.3.31. The matrix A defined in Problem 29 in Section 4.3.123 51 3 4 2246 -132. A =41. Consider the vectors01A₁ = [2 ~]-42= [-2 1] -4 = [19]A1A2A32in M₂ (R). Determine span{A₁, A2, A3}.42. Consider the vectors2 nes m spankP1, P2J.12^-[43]^2-[73]A2-1A₁ ==1 −1in M₂ (R). Find span{A1, A2}, and determine whetheror not Blies in this subspace.1[34]43. Let V = C(I) and let S be the subspace of Vspanned by the functionsf(x)=coshx, g(x) = sinhx.(a) Give an expression for a general vector in S.(b) Show that S is also spanned by the functionsh(x) = e*, j(x) = e¯x.

Accepted Answer

Answered: Image /qna-images/answer/f1cd3ca2-f5b9-4e02-a404-dfe29de775d4.jpg

For Problems 25-33, determine a spanning set for the null space of the given matrix A.