18. Two matrices A and B are said to anticommute if AB = - BA. If A and B are anticommuting 3 × 3 matrices, show that one or the other is noninvertible. %3D
18. Two matrices A and B are said to anticommute if AB = - BA. If A and B are anticommuting 3 × 3 matrices, show that one or the other is noninvertible. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plz solve question 18 with explanation within 30-40 mins
![18. Two matrices A and B are said to anticommute if AB = - BA. If A and B are
anticommuting 3 × 3 matrices, show that one or the other is noninvertible.
5. Three bodies having masses m,, m2, and m; are placed at the respective points
(-1,1), (-1, – 1), and (2, 1). Suppose that the center of gravity of the configura-
tion is at (0,0), and that the sum of the masses is 1. Find m1, m2, and m3.
1. The following is a list of sets with operations of addition and scalar multiplication
defined on them. For each set, show that the set, together with its indicated
operations, forms a vector space over the reals.
(b) The real matrices of the form
[: :]
with the usual addition and scalar multiplication.
(g) Differentiable functions on the interval (0,1) with
(f + 8)(x) = f(x) + g(x)
(af)(x) = a( f(x))
(the usual addition and scalar multiplication for functions)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c0b759e-a00a-4e23-b6db-9f4dc657f8b7%2F68429bd3-2da8-4b24-a355-7e4171e70bf4%2Fz1264l_processed.png&w=3840&q=75)
Transcribed Image Text:18. Two matrices A and B are said to anticommute if AB = - BA. If A and B are
anticommuting 3 × 3 matrices, show that one or the other is noninvertible.
5. Three bodies having masses m,, m2, and m; are placed at the respective points
(-1,1), (-1, – 1), and (2, 1). Suppose that the center of gravity of the configura-
tion is at (0,0), and that the sum of the masses is 1. Find m1, m2, and m3.
1. The following is a list of sets with operations of addition and scalar multiplication
defined on them. For each set, show that the set, together with its indicated
operations, forms a vector space over the reals.
(b) The real matrices of the form
[: :]
with the usual addition and scalar multiplication.
(g) Differentiable functions on the interval (0,1) with
(f + 8)(x) = f(x) + g(x)
(af)(x) = a( f(x))
(the usual addition and scalar multiplication for functions)
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