examples of the following matrices. We 39. A 2 x 2 matrix that has a nullspace consisting only of the zero vector. 40. A 2 x2 matrix that has a nullspace with a basis consisting of one non-z...
36. (a) Every 2 X 2 stochastic matrix has at least one steady state vector. (b) If A and B are stochastic matrices, then so is ½ (A + B).
4. For this question, we define the following matrices: 1-2 0 To 61 C= 0 -1 2 , D= 3 1 . [3 24 L-2 -1] (a) For each of the following, state whether or not the expression can be evaluated. If it can be, evaluate it. If it cannot be, explain why. i. B? +D ii. AD iii. C + DB iv. CT-C (b) Find three distinct vectors X1, X2, X3 such that Bx; = 0 for i =...
please help me with questions 1,2,3 1. Let V be a 2-dimensional vector space with basis X = {v1, v2}, write down the matrices [0]xx and [id]xx. 2. Let U, V, W be vector spaces and S:U +V, T:V + W be linear transforma- tions. Define the composition TOS:U + W by To S(u) = T(S(u)) for all u in U. a. Show that ToS is a linear transformation. b. Now suppose U is 1-dimensional with basis X {41}, V...
Problem 4. Let GL2(R) be the vector space of 2 x 2 square matrices with usual matrix addition and scalar multiplication, and Wー State the incorrect statement from the following five 1. W is a subspace of GL2(R) with basis 2. W -Ker f, where GL2(R) R is the linear transformation defined by: 3. Given the basis B in option1. coordB( 23(1,2,2) 4. GC2(R)-W + V, where: 5. Given the basis B in option1. coordB( 2 3 (1,2,3) Problem 5....
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
some useful examples the 1st one is the question where x is a vector while the second are examples. (d) Now consider the N-dimensional vector x an the integral ((22%)lejbTA-lb. (23.46) det A By differentiating with respect to components of the vector b, and then setting b 0, show that (r,a) (23.47) (e) Using these results, argue that +(A)u(A (23.48) j k. (f) Write down an expression for the general case Ti.z) This is the basis of Wick's theorem in...
Question 5 [3+(2+4) marks] (a) The matrix A has a repeated eigenvalue of 1 = 2. During the solution of the solution (A-21)X = 0, the augmented matrix below appears. Find a basis for the eigenspace for this eigenvalue. Ti 0 -2 07 lo o o lo To ooo (b) (i) Show that if T(x) is a linear transformation from R" to R", that T(0) is the zero vector. (i) Assume that T(u) = 0 only when u = 0....
I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
2. Consider the following set of complex 2 x 2 matrices where i = -1: H = a + bi -c+dil Ic+dia-bi Put B = {1, i, j, k} where = = {[ctdie met di]|1,3,c,dex} 1-[ ), : = [=]. ; = [i -:], « =(: :] . (a) Show that H is a subspace of the real vector space of 2 x 2 matrices with entries from C, that is, show H is closed under matrix addition and multi-...
The area of the parallelogram formed by vectors a=(−1,3,1) and b=(1,2,0), rounded to one decimal, is: Select one: a. 5.4 b. 5.5 c. -6.0 d. none of above Find the component of the vector with initial point (2,−1,1) and terminal point (4,3,−6): Select one: a. (2,4,−7) b. (6,3,−5) c. (8,−3,−6) d. (−2,−4,7) Determine whether the statement is True or False: The sum of two invertible matrices of the same size must be invertible. Select one: a. True b. False Determine...