In matrix notation, the kets | +>. | -> are represented by In matrix notation, the...
Use Dirac notation(the properties of kets, bras, and inner products) directly without explicitly using matrix representations to establish that the projection operator P _+ is Hermitian. Use the fact that P^2_+ = P _+ to establish that the eigenvalues of the projection operation are 1 and 0.
Given a matrix A, determine the matrix represented by 3A. -9-9 A= -9 0 ЗА = Use the following matrices to compute A+B. 02 5 1 0 A= B= 1 1 4 - 1 4 - 1 A+B= For the indicated function, find the values f(-9), f(0), and f(4). x, if x < 0 f(x) = 8x + 6, if x 20 f(- 9) = f(0) = f(4)=0
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. - 2(4x-5)<2 Choose the correct and per below that is the solution set to the inequality O A. {x[x> 1} or (1,00) OB. {x\x < 1) or (-0,1) O C. {x}x< - 1} or [-00,- 1] OD. {x[x> 1} or [1.00]
13. Draw the directed graph represented by the given adjacency matrix adj and the data matrix data. <6> 0111 Adj = 0011 0001 CAT data = RAT BAT DOG 0110
a) b) c) d) The interval notation (-3, 1) described in set builder notation is {* | -3 5xs1} {x-3<x<1) {x-35x<1} {x|-3<x51} The set-builder notation {xl-55x<8} is equivalent to (-5,8) O(-5, 8] O [-5,8) O [-5, 8] To solve 2x - 11<3, one must consider only one case two different cases three different cases O four different cases If f(x) = 3x2 and g(x) = x + 2, then (gf)(x) is 3x2 + 2 3x3 + 6x2 03x2 + x...
For the circuit represented in Fig. 9.54,(a) obtain an expression for uC(t) valid for all t> 0. (b) Determine uC at t 10 ms and t 600 ms. (c) Verily your answers to part (b) with an appropriate PSpice simulation. 1? 0.01 H I-0 5? FIGURE 9.54
`1) How is -9 (base 10) represented in 8-bit two's complement notation? a) 00001001 b)11110111 c)11110110 d) 11111001 2) The binary addition of 1 + 1 + 1 + 1 = A) 1111(base 2) b) 0001(base2) C) 0100(base2) D) 1001(base2) 3) How is –1 (base 10) represented in 8-bit two's complement notation? A) 1111111- B) 111111111 C) 00000001 D) 00000010
6. Matrix Calculations: Consider the linear tre tions: Consider the linear transformation represented by the matrix (a) {5 points) Compute the eigenvalues of A. (b) {10 points) Compute the eigenvectors of A. 1 points is the state space system = Ag internally anymptotically stabler Explain.
3) Solve the following inequality. Express the solution using interval notation. 2x +1 <0 Answer
, 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