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- 2. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks.arrow_forward1. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks.arrow_forwardAssume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the abovearrow_forward
- Q1/Details of square footing are as follows: DL = 800 KN, LL = 500 kN, Fy=414 MPa, Fc = 20 MPa Footing, qa = 120 kPa, Column (400x400) mm. Determine the dimensions of footing and thickness? Q2/ For the footing system shown in Figure below, find the suitable size (BxL) for: 1. Non uniform pressure, 2. Uniform pressure, 3.Uniform pressure with moment in clockwise direction. (Use qmax=qall =200kPa). Property, line M=200KN.m 1m P-1000KNarrow_forwardRefer to page 52 for solving the heat equation using separation of variables. Instructions: • • • Write the heat equation in its standard form and apply boundary and initial conditions. Use the method of separation of variables to derive the solution. Clearly show the derivation of eigenfunctions and coefficients. Provide a detailed solution, step- by-step. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forwardAssume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the abovearrow_forward
- Let H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardRefer to page 20 for orthogonalizing a set of vectors using the Gram-Schmidt process. Instructions: • Apply the Gram-Schmidt procedure to the given set of vectors, showing all projections and subtractions step-by-step. • Normalize the resulting orthogonal vectors if required. • Verify orthogonality by computing dot products between the vectors. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 54 for solving the wave equation. Instructions: • Apply d'Alembert's solution method or separation of variables as appropriate. • Clearly show the derivation of the general solution. • Incorporate initial and boundary conditions to obtain a specific solution. Justify all transformations and integrations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 14 for calculating eigenvalues and eigenvectors of a matrix. Instructions: • Compute the characteristic polynomial by finding the determinant of A - XI. • Solve for eigenvalues and substitute them into (A - I) x = 0 to find the eigenvectors. • Normalize the eigenvectors if required and verify your results. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardExilet x = {a,b.c}dex.x―R> d(a,b) = d(b, c)=1' d(a, c) = 2 d(xx)=0VXEX is (x.d) m.s or not? 3.4 let x= d ((x,y), (3arrow_forwardHiw Show that sup (0,1) = 1 الفصل الثاني * Dif: let {an} be Seq. then fan?arrow_forward
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