Question 2 [6 points] Consider the matrix defined below and answer the following questions. A = [−1 3 0 2 5 1 0 1 −7] (a) [4 points] The inverse of the matrix above can be expressed as A−1 = 1 78[a b c d 7 f g h −11] Use the Inversion Algorithm to find the missing entries. (b) [2 points] Use your answer from part (a) to solve the system Ax = b where x = (x1, x2, x3) and b = (1, −1, 0).
![Question 2 [6 points] Consider the matrix defined below and answer the following questions. A = [−1 3 0 2 5 1 0 1 −7] (a) [4 points] The inverse of the matrix above can be expressed as A−1 = 1 78[a b c d 7 f g h −11] Use the Inversion Algorithm to find the missing entries. (b) [2 points] Use your answer from part (a) to solve the system Ax = b where x = (x1, x2, x3) and b = (1, −1, 0).](https://www.doubtrix.com/uploads/editor/7386247581aRsctTsgFp.png)
![Let A = [1 -4 -3 -4 4 0 2 4 6] and b = [b1 b2 b3] Show that the equation Ax = b does not have a solution for all possible b, and describe the set of all b for which Ax = b does have a solution. How can it be shown that the equation Ax = b does not have a solution for all possible b? Choose the correct answer below. A. Find a vector b for which the solution to Ax = b is the zero vector. B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. C. Find a vector x for which Ax = b is the zero vector.
D. Row reduce the matrix A to demonstrate that A has a pivot position in every row. E. Row reduce the augmented matrix [ A b ] to demonstrate that [ A b ] has a pivot position in every row. Describe the set of all b for which Ax = b does have a solution. Type an expression using b1, b2, and b3 as the variables and 1 as the coefficient of b)](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1700960889-Q7.JPG)
![Question 2 Apply what you know about conservation laws to the following questions. (a) Two protons are held fixed on the y-axis at y = a and y = −a. You release an electron (mass me) on the x-axis at x = 2 a. What is the maximum speed the electron will reach? (b) An electron (mass me) and proton (mass mp) are held a distance r apart. They are released simultaneously and begin to accelerate towards each other. What is the electron's speed by the time the distance between the charges has halved? Answers: (a) vmax = [e2 ameπϵ0(1−15)]1 /2 (b) ve = [14πϵ02 e2 mpme(me+mp)r]1 /2 Question 3 (a) Show that the electric field inside a solid charged sphere with a uniform charge density of ρ is E→(r→) = ρr→/(3ϵ0). Here r→ is a position vector relative to the centre of the sphere. Use known results for spherically symmetric charge distributions. (b) Suppose a spherical cavity is hollowed out of the sphere. The centre of the cavity is at position a→ relative to the centre of the sphere. Derive an expression for the electric field inside the cavity. You should find that it is perfectly uniform. Hint: Use your result in (a) together with the superposition principle.](https://www.doubtrix.com/uploads/editor/9839175511KTRtNuwhVd.jpg)
