Linear algebra matrices multiplication (transpose)

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SUMMARY

The discussion focuses on the multiplication of matrices and the properties of transposition, specifically the equation (A^transpose)^transpose = A. Participants explore the process of finding the transpose of a matrix, using the example matrix A = [[-5, 0], [-8, -7]]. The conversation emphasizes simplifying expressions involving transposed matrices, ultimately leading to the conclusion that the transposition operation can be reversed. Key steps include manipulating the expression ((2A - I)^T)^T and applying matrix operations to derive the final result.

PREREQUISITES
  • Understanding of matrix transposition
  • Familiarity with matrix operations (addition, multiplication)
  • Knowledge of identity matrices
  • Basic linear algebra concepts
NEXT STEPS
  • Study the properties of matrix transposition in detail
  • Learn about identity matrices and their role in matrix operations
  • Explore advanced matrix multiplication techniques
  • Investigate applications of linear algebra in computational problems
USEFUL FOR

Students studying linear algebra, educators teaching matrix operations, and anyone interested in understanding the mathematical foundations of matrix transposition and multiplication.

dmoney123
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Homework Statement



We are looking for the matrix A

Homework Equations



(A^transpose)^transpose=A

The Attempt at a Solution



i would start with finding the transpose of the matrix.

-5 0
-8 -7
 

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dmoney123 said:

Homework Statement



We are looking for the matrix A

Homework Equations



(A^transpose)^transpose=A

The Attempt at a Solution



i would start with finding the transpose of the matrix.

-5 0
-8 -7

OK, so
((2A - I)^T)^T = \begin{bmatrix}-5&0\\-8&-7\end{bmatrix}

Now what? Use your relevant equation to simplify the left side.
 
S0 + identity matrix on left side... =

[-4 0] ... then /2= [-2 0]
-8 -6 ......-4 -3

GOT IT!
 
Last edited:

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