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e-30 sin() -1 backward substitution method 4. Given A = sin(t) cos(t) tanto find the following...
Given ? = a. Matrix of minors (2pts) b. Matrix of cofactors (2pts) c. Adjoint matrix...
Given ? =
a. Matrix of minors (2pts)
b. Matrix of cofactors (2pts)
c. Adjoint matrix (2pts)
d. Determinant of A (2pts)
e. Inverse of A using the Adjoint matrix. (2pts)
Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos...
Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos sin A = [ cose sin e sin e 0 cos e - cos ]
1 EXERCISE 5.2 1. Evaluate the following determinants:
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
Assume sin S = {}, cos S = 4, sin T = 1, cos T =...
Assume sin S = {}, cos S = 4, sin T = 1, cos T = Find the given quantities without using a calculator. Give answer as a fraction (for instance on half would be written 1/2) Sin (S +T)= Cos (S+T)=
6. Find the minors and cofactors of the third row, given 9 11 4 A= 3...
6. Find the minors and cofactors of the third row, given 9 11 4 A= 3 27 6 10 4 4. Find the inverse of each of the following matrices: 4 -2 1 100 (a) E = 7 3 0 (CG= 0 0 1 2 0 1 0 1 0 -1 2 100 (6) F= 03 (d) H= 0 1 0 4 02 0 0 1 1
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t <...
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz...
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos...
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos x 0, 0 0 1 cose 0 sin 0] O(0) 4 0 1 0 , 1-sin 0 cos e ſi 0 0 1 0(0) 4 0 cos – sin 0, 0 sinº cos 0 ] are rotation matrices, that is, V-7(4) = \T(4), 6-7(0) = OT(0), $ER, 6-7(0) = $1(0), and det(\())) = 1, det(O(0)) = 1, det($(0)) = 1. Prove also that R321(4,0,0)...
solve these recurrences using backward substitution method: a- T(n)=T(3n/4)+n b-T(n) = 3 T(n/2) +n
solve these recurrences using backward substitution method: a- T(n)=T(3n/4)+n b-T(n) = 3 T(n/2) +n
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of...
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
Given ? =
a. Matrix of minors (2pts)
b. Matrix of cofactors (2pts)
c. Adjoint matrix (2pts)
d. Determinant of A (2pts)
e. Inverse of A using the Adjoint matrix. (2pts)
Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos sin A = [ cose sin e sin e 0 cos e - cos ]
Assume sin S = {}, cos S = 4, sin T = 1, cos T = Find the given quantities without using a calculator. Give answer as a fraction (for instance on half would be written 1/2) Sin (S +T)= Cos (S+T)=
6. Find the minors and cofactors of the third row, given 9 11 4 A= 3 27 6 10 4 4. Find the inverse of each of the following matrices: 4 -2 1 100 (a) E = 7 3 0 (CG= 0 0 1 2 0 1 0 1 0 -1 2 100 (6) F= 03 (d) H= 0 1 0 4 02 0 0 1 1
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
VER, DER, 4) Prove that the rotation matrices [cos – sin 07 1(0) 4 sinŲ cos x 0, 0 0 1 cose 0 sin 0] O(0) 4 0 1 0 , 1-sin 0 cos e ſi 0 0 1 0(0) 4 0 cos – sin 0, 0 sinº cos 0 ] are rotation matrices, that is, V-7(4) = \T(4), 6-7(0) = OT(0), $ER, 6-7(0) = $1(0), and det(\())) = 1, det(O(0)) = 1, det($(0)) = 1. Prove also that R321(4,0,0)...
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
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