Project ForgeEngineering Mathematics
Linear Algebra
GATE 2020
Medium
A matrix P is decomposed into its symmetric part S and skew symmetric part V. If S = [[−4,4,2],[4,3,7/2],[2,7/2,2]] and V = [[0,−2,3],[2,0,7/2],[−3,−7/2,0]], then matrix P is
- A[[−4,6,−1],[2,3,0],[5,7,2]]
- [[−4,2,5],[6,3,7],[−1,0,2]]
- C[[4,−6,1],[−2,−3,0],[−5,−7,−2]]
- D[[−2,9/2,−1],[−1,81/4,11],[−2,45/2,73/4]]
Explanation
Since P = S + V, add element-by-element: row 1: (−4+0, 4−2, 2+3) = (−4, 2, 5); row 2: (4+2, 3+0, 7/2+7/2) = (6, 3, 7); row 3: (2−3, 7/2−7/2, 2+0) = (−1, 0, 2). This matches option (B) exactly.
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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