Find matrix X satisfying the following equation, if possible. If it is not possible, say why. Find two solutions if there exist more than one.
Ax = B
A=
0 | 1 | -1 |
2 | 2 | 2 |
3 | 2 | -3 |
B =
4 | -1 |
2 | 4 |
1 | 5 |
Find matrix X satisfying the following equation, if possible. If it is not possible, say why....
Given the set of information, find a linear equation f(x) satisfying the conditions, if possible. (If not possible, enter IMPOSSIBLE.) f(−4) = 6 and f(5) = 3
6. (42 bonus each) Give a specific example (with numbers) of a matrix M satisfying the given conditions, or explain why no such matrix can exist. (Hint: If such a matrix is possible, give an example in rou echelon form.] (a) M is of size 6 x 4 and rank(M) = 3. (b) M is of size 4 x 6 and rank(M)=5.
Find the equation of the line satisfying the given cond possible. 43. Through (-1, 4), parallel to x + 3y = 5 45. Through (1,6), perpendicular to 3x + 5y = 1 47. Through (-5, 7), perpendicular to y = -2 49. Through (-5, 8), parallel to y = -0.2x + 6
For problems 4) and 5) answer the following (a) Does the equation Ax = 0 have a nontrivial solution? (b) Does the equation Ax = b have at least one solution for every possible b? 4) A is a 4 x 4 matrix with three pivot positions. 5) A is a 3 x 2 matrix with two pivot positions.
4. (15 marks) Consider the following equation: where i denotes the complex number satisfying i2--1 (a) Rewrite the number -i in the exponential form and transform equation (5) into (b) Solve (6) to get the five solutions wo, ..., wa and draw them on the Argand diagramme (c) Show that wo··· , ua are the eigenvalues of the following real-valued matrix 0 0 0 0 0 cos(2m/5) A-10 -sin2(2π/5) 0 0 cos(2π/5) 0 0 0 2cos(4π/5) 2 Hint: compute the...
5. Find a matrix A with the following properties or explain why it cannot exist: (a) A is a 3 x 4 matrix with rank 2 and 3 Null(A) = span { (b) A is a 4 x 4 matrix with nullity 2 and 3 Col(A) = span 5 (c) A is a 3 x 4 matrix with nullity 2 and 3 Col(A) = span 5
Given the set of information, find a linear equation satisfying the conditions, if possible. (If not possible, enter IMPOSSIBLE.) passes through (x, y) = (2, 8) and (x, y) = (5, 14) y = _______
5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The column space contains (1, 1,0, 1) and (0, 1, 1,-1) and whose null space contains (1,0,1,1) and (0,1,-1,0)7 5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The...
For each of the following cases, provide an example satisfying the stated property, or state why it is impossible. (a) (b) A 2 x 2 matrix with singular values 1 and 2 so that ||A@1|| = 5. A 3 x 3 matrix with 3 real distinct eigenvalues so that 0 is an eigenvalue of A2 + 13.
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...