The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is

Given: \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] \[A^T = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}^T \] \[ = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] \[ = A\]

The matrix A = ⎡ ⎢ ⎣ 1 0 0 0 2 0 0 0 4 ⎤ ⎥ ⎦ is - Mathematics

Question

The matrix $A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{matrix}]$ is

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identity matrix
symmetric matrix
skew-symmetric matrix
diagonal matrix

MCQ

Solution

Given:

$A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{matrix}]$

$A^{T} = {[\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{matrix}]}^{T}$

$= [\begin{matrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{matrix}]$

$= A$

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Symmetric and Skew Symmetric Matrices

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Q 45 Q 44 Next

Chapter 5: Algebra of Matrices - Exercise 5.7 [Page 69]

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Chapter 5 Algebra of Matrices
Exercise 5.7 | Q 45 | Page 69

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The matrix A = ⎡ ⎢ ⎣ 1 0 0 0 2 0 0 0 4 ⎤ ⎥ ⎦ is - Mathematics

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