Check whether (x + 1)² = 2(x − 3) is a quadratic equation.
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⚡ Key Formulas at a Glance
Formula (Hover/Click)
Cramer's Rule (3D System)
x = Δx/Δ, y = Δy/Δ, z = Δz/Δ (Δ≠0 unique, Δ=0 infinite/no sol)
Formula (Hover/Click)
Characteristic Equation
|A − λI| = 0 ⇒ Cayley-Hamilton Theorem A satisfies own eq
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Adjoint Determinant
|adj(A)| = |A|ⁿ⁻¹, |adj(adj(A))| = |A|(n−1)²
Formula (Hover/Click)
Orthogonal Matrix
A × Aᵀ = Aᵀ × A = I ⇒ |A| = ±1
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Board Exam 20244 Marks
State the fundamental principles and key formulas for Matrices Determinants, and solve a standard 4-mark examination question.
▶ Show Detailed Solution
1. Write down all given parameters and state applicable definitions.
2. Substitute into the master formula for Matrices Determinants.
3. Evaluate step-by-step to obtain final answer.