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What are covariant and contravariant vectors? Show that acceleration is a contravariant vector.
Q. A second order tensor has components ■(2&1&0@1&-3&-1@0&-1&2) in OX1X2X3. The transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ is defined by X1’=1/3 (2x1+2x2-x3) X2’=1/3 (2x1-x2+2x3) X3’=1/3(-x1+2x2+2x3) (i)Find its components in the new system OX1’X2’X3’.(By using Matrix Formula). (ii) Compute A’32 in the new system.(By using component formula)
Q. Write transformation equations for a second order tensor Aij w.r.t this transformation and verify A’ii=Aii
WHAT IS MEAN BY (0,2) and (2,0) (1,1) tensor.
For the following matrix calculate the determinant: {{5,3,7},{1,0,1},{9,6,4}}
Evaluate the following: {{1,2,3},{4,5,6},{7,8,9}} * {{7,4},{6,4},{5,3}}
Given the following: A = 3 * 3 B = 2 * 4 C = 4 * 3 D = 3 * 2 Which of the following are defined: A * D D * B A * D^T C * D + A * D^T A * B A * D^T + C
Evaluate the following problem: 2*{{3,5},{7,9}} + 3*{{7,6},{5,4}} - 4*{{9,8},{7,6}}
Solve the system of simultaneous equations below using any of the matrix method 2x + 3y - z = 6 3x + y + 5z =8 x + 2y + z =10
4x + 2y + 3z. = 35 x + 3y + 2z. = 45 2x + y + 5z. = 28 Calculat value of x,y & z Crsmer's rule.
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