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Addition of Matrices
Addition of Matrices
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If [A] and [B] are two matrices of same order, [A] + [B] is defined as matrix formed by sum of corresponding elements.
Addition
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_8af0de3f0ea64b32bf85e9bccc7d8779~mv2.gif)
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_ddb619907b454730811ce162755f33ae~mv2.gif)
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_b60c27adc9c846068a6f1257f269adaa~mv2.gif)
Square Matrix as a Sum of Symmetric and Skew-Symmetric Matrix:
Symm+skew symm
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_d19ca3a6c1d4451fbfd6b57f3cb7ce59~mv2.gif)
where,
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_7eff25a6293f4f01be0de1ee0c5bf50f~mv2.gif)
(M + Trnas. of M) is a Symmetric matrix.
![GATE matrix algebra](https://static.wixstatic.com/media/85eba4_0e3cc711a49547ea8bf005a97cff42b6~mv2.gif)
(M - Trnas. of M) is a Skew-Symmetric matrix.
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In this way, any square matrix may be written as the sum of its symmetric and skew-symmetric parts.
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Example:
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GATE 2020: A matrix P is decomposed into its Symmetric part S and Skew-Symmetric part V. Find the matrix P.
Exmaples
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_af8be585d7bc4bfaa7a4a53acd90b0bb~mv2.gif)
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_c553f464e30e47dea81cc65e009f4cd0~mv2.gif)
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_c67b69547d5f4d3db2c1b98e60b44a2f~mv2.gif)
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_427eb70e672948388dd3d7ab5b846a5b~mv2.gif)
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_439811677cdc47fab6396cfbbf71bcab~mv2.gif)
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_685d82451695447c8e5a81c81d489af8~mv2.gif)
Solution:
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Matrix M = Symmetric part + Skew-Symmetric part
M = S + V
Adding S & V, M comes out to be
![GATE 2020 solved](https://static.wixstatic.com/media/85eba4_f09c42734f8847398dec7ba3d9b2af6d~mv2.gif)
So, B is the correct answer.
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