3. Let A = (-1 2 and B = 2 0 I. Compute tensor products A®B and B® A: II. Compute Hadamard products Ao B and Bo A: III. Compute A'•B and (A® B)`':

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Calculate the scalar triple product u (vx w), where u = . (Use symbolic notation and fractions where…

A: Here we have to evaluate the scalar triple product u. (v x w) .

Q: 3-2. Prove the triple scalar product identity А (Вх С) 3 (АХ В): С.

A:

Q: 2.1: Linear combinations. qy7 Jump to level 1 V1 = 9 a1 A2 = Which weights should be used for b = a₁…

A:

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

A:

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

A:

Q: 42. Rather than use the standard definitions of addition and scalar multiplication in R®, let these…

A: The given question can be solved as shown in step2.

Q: If vectors b, c and d are not coplanc then prove that vector

A:

Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: If A and B are vector fields, prove the following: V (A · B) = (B - V) A + (A · V) B+B× (V×A)+A ×…

A:

Q: 1. Consider the Cartesian tensors i) ii) Or Or.) (a) Identify their orders. (b) Rewrite them in…

A: Given the system

Q: 18 f1. are the corresponding Christoffel symbols and are components of two symmetric covariant…

A:

Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

A:

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

A:

Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

A:

Q: Find u ∙ (v × w). This quantity is called the triple scalar product of u, v, and w.u = (2, 0, 1), v…

A: Given, the three vectors u = (2, 0, 1), v = (0, 3, 0), w = (0, 0, 1). And we have to find the triple…

Q: If T is a mixed tensor, then T} + T{ is generally not a tensor a tensor May or may not

A: Answer : may or may not  Hence, Option (iii) is true.

Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C,…

A: Given statements, (i) In triple dot of vectors (A×B)·C=(B×A)·C where the vectors A,B, and C are not…

Q: 3. Demonstrate the following relationships involving the determinate (a) Vector cross product (b)…

A:

Q: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

A: