Show the following by vector (dyadic) and indicial operations in 3-D:
a) ?×??=0
b) ??×?=0
c) ?×(?×?)=??−??∙?
d) ?∙(?×?)=0
where: a=ai?i and ?=δij?i?j
Show the following by vector (dyadic) and indicial operations in 3-D: a) ?×??=0 b) ??×?=0 c)...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
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...
Use the Pumping Lemma to show that the following languages are not regular. (a){apaq | for all integers p and q where q is a prime number and p is not prime}. (b) {ai bj || i − j | = 3} (c) {ai bj ck | i = j or j 6= k} (d) {aibj | i/j is an integer}
Please make it simple and clear to understand 3. A vector field is given by (a) Show that the vector field r is conservative. Then find a scalar potential function f(r,y,) such that r - gradf and f(0,0,0) 0 (b) By the result of (a) the following line integral is path independent. Using the scalar potential obtained in (a) evaluate the integral from (0,0,2) (where-y-0) to (4,2,3) (where -1,y 0,2) 4.2,3) J(0,0,2) 3. A vector field is given by (a)...
explain option C ,D Let A, B, C and D be the following 4 x 4 binary matrices. 1 10 1 0 0 1 0 A= 10 0 1 0 0 0 0 B AT where cij= a4-i+1 j where d -4y] = a; 4-j+1 D = Match the following binary images to the given matrices A, B, C and D. No malch n Let A, B, C and D be the following 4 x 4 binary matrices. 1 10...
E 3 points The indicial equation of: x2y" + xy' + (x2 - 4)y = 0 is A)r? + 4 = 0 B) r2 - 4 = 0 C)r? - 4r = 0 D) r2 – 4r + 4 = 0 E)r2-r+4= 0 ОА B Ос OD OE 3 points TI futbe ODE. 1/ 21 sinhy is
pigeonhole 1. Show that in every sequence (ai,a2, a100) of the letters A,B,C,D, there are two indices 1i< j < 98 such that (ai, ai+1,aj+2) = (aj, aj+1, aj+2).
IN MATLAB Identify which of the following operations is valid. If invalid, e vector, c is a 4x1 vector, d is a 1x4 vector, E is a 6x4 matrix, and α is a scalar. xplain why. Assume: A is a 4x4 matrix, b is a 6 x1 i) d-S (ii) Ab-c (ii) Aac dT (iv) bEc-a (v) bd E
Simplify the following indicial expressions as much as possible. ΣΣ1C,B (a) Substitute Cii = -1 AipBpj into a = k 1 Hint: Consider changing the index j to index k in the expression for C;i 3 ( b) Σ-Σ_ Σ1 Α, Βιδικ - Σ Σ Σ-12AB , im rį=1 i=1 m=1 Hint: Use the index substitution property of Kronecker delta first to simplify the expression. When you do that, the triple summation will reduce to double summation in each symbol...
why is this wrong for vectors vector<char> decrypt{ {'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A'}, {'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'}, }; for(int...