A four vector [A] and a tensor [B] are defined by: [A] = (-2, 7, 1,3) 1 3 -5 7 0 2 0 -1 5 5 2 6 -3 -3 0 1 [BBY] = (a) Write down a general form for the tensor that results from each of the following expressions: (i) A¹Bij, (ii) A¹Bjk, and in each case state the rank and type of the resulting tensor. (b) Evaluate the expressions (i) A¹B₁, and (ii) A¹B;; for the case where where j = 1.
A four vector [A] and a tensor [B] are defined by: [A] = (-2, 7, 1,3) 1 3 -5 7 0 2 0 -1 5 5 2 6 -3 -3 0 1 [BBY] = (a) Write down a general form for the tensor that results from each of the following expressions: (i) A¹Bij, (ii) A¹Bjk, and in each case state the rank and type of the resulting tensor. (b) Evaluate the expressions (i) A¹B₁, and (ii) A¹B;; for the case where where j = 1.
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![A four vector [A] and a tensor [B] are defined by:
[A] = (-2, 7, 1, 3)
3
-5 7
2
0
-1
5 2 6
-3 0 1
[BBY] =
1
0
5
-3
(a) Write down a general form for the tensor that results from each of
the following expressions: (i) A'Bij, (ii) A¹Bjk, and in each case
state the rank and type of the resulting tensor.
(b) Evaluate the expressions (i) A¹B₁; and (ii) A¹B;; for the case where
where j = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7e6862b-b483-41de-846c-f25c452fd4a2%2F3d8fe0ce-d894-4b75-9e38-eb85b95f14a0%2Fht761hu_processed.png&w=3840&q=75)
Transcribed Image Text:A four vector [A] and a tensor [B] are defined by:
[A] = (-2, 7, 1, 3)
3
-5 7
2
0
-1
5 2 6
-3 0 1
[BBY] =
1
0
5
-3
(a) Write down a general form for the tensor that results from each of
the following expressions: (i) A'Bij, (ii) A¹Bjk, and in each case
state the rank and type of the resulting tensor.
(b) Evaluate the expressions (i) A¹B₁; and (ii) A¹B;; for the case where
where j = 1.
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