Questions: A=[9 2 6; -4 -5 -6] (A^T)^T=

A=[9 2 6; -4 -5 -6] (A^T)^T=
Transcript text: A=\left[\begin{array}{ccc}9 & 2 & 6 \\ -4 & -5 & -6\end{array}\right] \\ \left(A^{T}\right)^{T}=
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Solution

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Solution Steps

To solve this problem, we need to understand the properties of matrix transposition. The transpose of a transpose of a matrix returns the original matrix. Therefore, (AT)T=A(A^T)^T = A.

Step 1: Understanding Matrix Transposition

The problem involves the matrix A A given by: A=[926456] A = \begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix}

Step 2: Applying Transposition Properties

The property of matrix transposition states that the transpose of the transpose of a matrix returns the original matrix: (AT)T=A (A^T)^T = A

Step 3: Result Verification

Given the property, we verify that: (AT)T=[926456] (A^T)^T = \begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix}

Final Answer

[926456] \boxed{\begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix}}

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