5)Prove that CNOT|x>ly> = |x> |x op y>, where op is an exclusive OR operator and CNOT is the controll-not transformation/operator. Note that CNOT has a matrix representation. In your proof, verify only the cases where x-1.
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- Consider a 3×3 matrix M. Which of the following statements about M is false.1) M does not need to be diagonal to represent rotations.2) M can be a part of a homogeneous transformation.3) M can represent rotations.4) M can represent at most only one planar rotation. Consider the matrix D = [ e g 0 ] I f a b I [ 0 c d ] Which of the following should be true in orderfor D to represent a rotation about the x-axis of the coordinate system?1) f = g = 0, e = 1, a = −d, b = c.2) e = f = g = 0, a = −d, b = c.3) f = g = 0, e = 1, a = d, b = −c.4) e = f = 0, g = 1, a = d, b = c.Write down the tensor expression for the following matrix operations. Where A,B are 3 × 3, C is 3 × 4, and D is 4 × 7 matrices. And for a matrix M, its i-th row j-th column component will be denoted as M_ij . (a) det(A · B^T ).(b) Tr[A · B].(c) B · C · D, and explicitly spell out all the index summation.(d)δ_ii =?(e) ϵ_ijkϵ_ijk =?Consider the matrix multiplication C = AB. A matrix W is called a witness matrix with the following conditions: • If ci j = 0, then wi j = 0.• If ci j = 1, then wi j = k where aik = bkj = 1. make code to displays two Booelan matrices A and B and their productC. Note that we define these matrices with 0 and 1 entries and declare their typesas boolean with dtype = bool statement after specifying the entries. Alternatively,we could have specified theses matrices with True and False entries. The booleanproduct C is then converted to integer by the astype method and both forms of Care printed
- I do not understand this expression. so is c[i][j] += a[i][h] * b[h][j] mean c[i][j] = a[i][h] * b[h][j] + c[i][j]?? ; We do not know about the + matrix c right?we represent the finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C: a delay by one (i.e. a right shift) transforms the signal x = (xo X1 X2]" into x = [xı xo xz]" and it can be described by the matrix TO D = [0 1 0'0 0 1'1 0 0] so that x = Dx. Determine the matrix F that implements the one step difference operator in C ie the operator that transforms a signal x into [(x - x)(x1 - x0)(x2 - 1)]write a C++ program to Given a matrix of dimension m*n where each cell in the matrix can have values 0, 1 or 2 whichhas the following meaning:0: Empty cell1: Cells have fresh oranges2: Cells have rotten orangesSo we have to determine what is the minimum time required so that all the oranges becomerotten. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1],[i,j+1] (up, down, left and right). If it is impossible to rot every orange then simply return -1.Examples:Input: arr[][C] = { {2, 1, 0, 2, 1},{1, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges can become rotten in 2 time frames.Input: arr[][C] = { {2, 1, 0, 2, 1},Tahir Iqbal Department of Computer Sciences. BULC{0, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges cannot be rotten.Below is algorithm.1) Create an empty Q.2) Find all rotten oranges and enqueue them to Q. Also enqueuea delimiter to indicate beginning of next time frame.3) While Q is not empty do following3.a) While delimiter in…
- Simplify the following function: F (W, X, Y, Z) = ∑ (3, 5, 11, 15) with don't care conditions d = ∑(1, 2, 6, 9) . Make a four-variable k-map to simplify F.Type in Latex **Problem**. Let $$A = \begin{bmatrix} .5 & .2 & .3 \\ .3 & .8 & .3 \\ .2 & 0 & .4 \end{bmatrix}.$$ This matrix is an example of a **stochastic matrix**: its column sums are all equal to 1. The vectors $$\mathbf{v}_1 = \begin{bmatrix} .3 \\ .6 \\ .1 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \mathbf{v}_3 = \begin{bmatrix} -1 \\ 0 \\ 1\end{bmatrix}$$ are all eigenvectors of $A$. * Compute $\left[\begin{array}{rrr} 1 & 1 & 1 \end{array}\right]\cdot\mathbf{x}_0$ and deduce that $c_1 = 1$.* Finally, let $\mathbf{x}_k = A^k \mathbf{x}_0$. Show that $\mathbf{x}_k \longrightarrow \mathbf{v}_1$ as $k$ goes to infinity. (The vector $\mathbf{v}_1$ is called a **steady-state vector** for $A.$) **Solution**. To prove that $c_1 = 1$, we first left-multiply both sides of the above equation by $[1 \, 1\, 1]$ and then simplify both sides:$$\begin{aligned}[1 \, 1\, 1]\mathbf{x}_0 &= [1 \, 1\, 1](c_1\mathbf{v}_1 +…Algorithm to Canonicity predicate for a 0-1 matrix.
- 6. Let M = (Q,Sigma,s, q0, F) be a dfa and define cfg g= (v,sigma, R,S) as follows: 1. V=Q; 2. For each q in Q and a in sigma, define rule q->aq' where q' = s(q,a); 3. S = q0 Prove L(M) = L(G)Answer the given question with a proper explanation and step-by-step solution and don't copy past from online source. Find an optimal parenthesization and the minimum number of scalar multiplications needed for a matrix-chain product whose sequence of dimensions is (5,10,3,12,5,50. Show all the steps used to arrive at the solution.Construct a Playfair matrix with the key "occurrence". Make a reasonable assumption about how to treat redundant letters in the key.