GATE 2024 ST – Question 15

Matrix Theory · Inner Products and Quadratic Forms · 1 mark · Multiple choice

In standard ℝ², u=(a,b)ᵀ has inner products 2 with (1,2)ᵀ and −1 with (4,−2)ᵀ. Which holds?

Show answer and explanation

Correct answer: (D) u·(−1/2,1)=4/5

Explanation

Solve a+2b=2,4a−2b=−1 to get a=1/5,b=9/10. Then u·(−1/2,1)=−1/10+9/10=4/5. The other listed dot products are −7/10,7/10,−1/20 respectively. **D**.

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