MUST use A times indetity matrix method to prove it is not possible and explain why it is ntot possible by looking the matrix turns out
DO NOT use determine method 4-4 =0 is not possible!!!
2 | 1 |
4 | 2 |
add the Identity Matrix to the right
2 | 1 | 1 | 0 |
4 | 2 | 0 | 1 |
Divide row1 by 2
1 | 1/2 | 1/2 | 0 |
4 | 2 | 0 | 1 |
Add (-4 * row1) to row2
1 | 1/2 | 1/2 | 0 |
0 | 0 | -2 | 1 |
Divide row2 by -2
1 | 1/2 | 1/2 | 0 |
0 | 0 | 1 | -1/2 |
Add (-1/2 * row2) to row1
1 | 1/2 | 0 | 1/4 |
0 | 0 | 1 | -1/2 |
Last row of a matrix is zero so, The rows and columns are not independent. so matrix is not invertible
MUST use A times indetity matrix method to prove it is not possible and explain why...
4. Use elementary row operations (Gauss-Jordan method) to find the inverse of the matrix (if it exists). If the inverse does not exist, explain why. 1 0-1 A:0 1 2 0 -1 2us 0P 0 Determine whether v is in span(ui, u2, us). Write v as a linear combination of ui, u2, and us if it is in span(u1, u2, u3). If v is not in span(ui, u2, u3), state why. span(ui,u2,us). If v is not in span(ui,u^, us), state...
5. Let f(x) = ax2 +bx+c, where a > 0. Prove that the secant method for minimization will terminate in exactly one iteration for any initial points Xo, X1, provided that x1 + xo: 6. Consider the sequence {x(k)} given by i. Write down the value of the limit of {x(k)}. ii. Find the order of convergence of {x(k)}. 7. Consider the function f(x) = x4 – 14x3 + 60x2 – 70x in the interval (0, 2). Use the bisection...
Part 1 Part 2 7.1.2. Let R be a commutative ring and a, b E R, and define The goal of this problem is to prove that (a, b) is an ideal of R (a) Explain how you know that 0 E (a, b b) What do two random elements of (a, b) look like? Explain why their sum must be in (c) For s E R and z E (a,b), explain why sz E (a, b). 7.2.1. In the...
(6) Let A denote an m x n matrix. Prove that rank A < 1 if and only if A = BC. Where B is an m x 1 matrix and C is a 1 xn matrix. Solution (7) Do the following: (a) Use proof by induction to find a formula for for all positive integers n and for alld E R. Solution ... 2 for all positive (b) Find a closed formula for each entry of A" where A...
, then n lim Let Ά be a square matrix. Prove that if ρ(A)<1 Use the following fact without proof. For any square matrix A and any positive real number ε , there exists a natural matrix norm I l such that l-4 ll < ρ (d) +ε IIA" 11-0
16. Diagonalize the following matrices if possible. (If not possible explain why not) Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= [-2 3 1-9 10 -1 15 4 -2 10. 2=4
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
(1 point) Let A = -3 -1 6 -4 0 6 -2 -1 5 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= D= Is A diagonalizable over R? choose Be sure you can explain why or why...
please solve parts a, b, c for this question 1 A = -1 1 (a) Suppose that is any nonzero vector in R2. Explain why the vectors U, AU, and A2 must be linearly dependent. (Note: do not use any numerical examples in your answer; your reasoning must be valid no matter what is.) s in the cpak of the ImlA) Thuscan be uvi Hen os a linear combo of the basi vetus op im{A) (b) Let Part (a) shows...
Ques 3 (d) Suppose that n-10, and Xi Xio represent the waiting times that the 10 people must wait at a bus stop for their bus to arrive. Interpret the result of (c) in the context of this scenario be iid observations from the Uniform(0,0) distribution. 3. Again, let X..., X (a) Find the joint pdf of Xu) and X() (b) Define R = X(n)-X(1) as the sample range. Find the pdf of R. (e) It turns out, if X...