Project ForgeEngineering Mathematics
Linear Algebra
GATE 2009
Medium
For a matrix [M] = [[3/5, 4/5], [x, 3/5]], the transpose of the matrix is equal to the inverse of the matrix, [M]ᵀ = [M]⁻¹. The value of x is given by
- -4/5
- B-3/5
- C3/5
- D4/5
Explanation
[M]ᵀ=[M]⁻¹ means M is orthogonal, so its rows are unit vectors and mutually orthogonal. Row 1 (3/5,4/5) already has norm 1. Row 2 (x,3/5) needs x²+9/25=1 ⟹ x=±4/5, and orthogonality of the rows requires (3/5)x+(4/5)(3/5)=0 ⟹ x=-4/5.
Source: GATE ME 2009 (2009)
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