21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3...
4. Find a basis for the solution space of the homogeneous linear system (aka find the basis for the null space), and then find the dimension of that space. 21 2+230 2x1+x2 + 3x3 = 0 21-6r2 +230 31-92 +330
=0 1. Find a basis for the solution space of the homogeneous linear system and find its dimension. 2 -34, +13 2x; -6x9 +223 =0 3x; -92, + 3x3 = 0
2. a) Find the dimension of the solution space of the homogeneous linear system (1 point) x-3y + z = 0 2x-6y + 2z = 0 2x + 4y-82=0 b) Find a basis for the solution space. (1 point)
Explain how to find a basis for the solution space of the homogeneous system 21 +5.7, +423 +70, +9:15 = 0 2 +5.29 + 5.03 +974 + 12.25 = 0 2.21 + 10.22 +673 + 10.04 + 12.25 = 0
Problem 1 (14 points) (a) Find the general solution to a third-order linear homogeneous differential equation for y(1) with real numbers as coefficients if two linearly independent solutions are known to be e-21 and sin(3.c). e (b) Determine that differential equation described in part (a).
Problem 1 (14 points) (a) Find the general solution to a third-order linear homogeneous differential equation for y(1) with real numbers as coefficients if two linearly independent solutions are known to be e-21 and sin(3.c). e (b) Determine that differential equation described in part (a).
2. Find the basis for the solution space of the homogeneous system: a. X+2y = 0 2x+4y=0 b. 3x+2y+4z=0 2x+ y - 2 = 0 x +y +3z =0
1. Graph the system of linear equations. Solve the system and interpret your answer 3y 2 -+2y 3 2. Solve the system of linear equations for and y (Cos ) x(sin 0) y = 1 (sin 0) x (cos 0) y = 1 3. Use back substitution to solve the system. 6r23r =-3 r22r3 1 3-2 4. Slove the given system by Gaussian elimination.. 4x1-2+x3-1 +2x2-3r3 = 2 2x 3= 1 5. Identify the element ary row operation (s) being...
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general solution to (4 (b) Find a fundamental set S of solutions of (Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general...
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the solution set of the homogeneous linear systems. 2. X1 + x2 + x3 = 0 X1 – X2 – X3 = 0 3. x1 + 3x2 + x3 + x4 = 0 2xı – 2x2 + x3 + 2x4 = 0 x1 – 5x2 + x4 = 0 X1 + 2x2 – 2x3 + x4 = 0 X1 – 2x2 + 2x3 + x4...