A matrix function A and a vector function b are given. Write the system of equations corresponding to x' = A(t)x + b(t). A(t)=3x3 matrix, b(t)=3x1 matrix Let u = (matrix 4 & -1 & 4) and A = (matrix 2, 5, -1 & 0, 1, -1 & 1, 2...
Recall that F^X becomes a vector space over F if we define addition and scalar multiplication by: f + g: x mapsto f(x) Let A= \left \{ -3, -2, -1, 0, 1, 2, 3, 4, 5 \right \} and define a relation ...
Use the definition to show that the set E - \{a + b \sqrt{-1}: a, b \epsilon Q \} is a vector space over Q. Let A and B be ideals of some ring R , and let I = left ( a + b : a epsilon A, b epsilon B right ) . If R = mathbb(Z), A = 4...
Show that v_1 = (3, -2), v_2 = (4, 3) span R^2 by expressing (x_1, x_2) as a linear combination of v_1 and v_2 for any given (x_1, x_2) in R^2., Express the vector v = (6, -7) as a...