Matrices all thinking style

All matrices things are here.

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• Question :

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1. Symmetric & Skew-Symmetric Matrices

18 is not important.

• Used in: Q1, Q13, Q18

• Concept: A matrix A is symmetric if A = Aᵗ, skew-symmetric if A = -Aᵗ.

• Symmetric and Skew-Symmetric Matrices

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2. Singular & Non-Singular Matrices

• Used in: Q2, Q6

• Concept: A matrix is singular if det(A) = 0.

• Singular vs Non-Singular Matrix | Math Antics

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3. Determinants

• Used in: Q2, Q3, Q6, Q7, Q14, Q20

• Concept: Determinants are scalar values used to determine invertibility.

• Determinants for Beginners | 3x3 Shortcut | ProfRobBob

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4. Matrix Inversion

• Used in: Q5, Q12, Q17, Q25

• Concept: For A⁻¹ to exist, det(A) ≠ 0; found using adjoint/determinant or row operations.

• Inverse of a 3x3 Matrix Using Adjoint | 10 Minutes

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5. Orthogonal Matrices

• Used in: Q15, Q19

• Concept: A matrix A is orthogonal if AᵗA = I.

• Orthogonal Matrices ( watch till 3.43 min )

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6. Matrix Multiplication

• Used in: Q21, Q22, Q23

• Concept: Multiply rows of first matrix with columns of second.

• Matrix Multiplication

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7. Matrix Equation Identity and Powers

• Used in: Q16, Q23

• Concept: Powers and polynomials in matrix equations (A², Aⁿ, etc).

• Matrix Powers and Equation (watch till 4.52 and If you want can try the question too that is till 10:00 )

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8. Cramer’s Rule

• Used in: Q14, Q20

• Concept: Solving linear systems using determinants.

• Cramer's Rule (3x3)

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9. Solving Systems Using Matrix Inversion

• Used in: Q12, Q17, Q25

• Concept: AX = B ⟹ X = A⁻¹B

• Solve Linear Equations Using Inverse Matrix

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10. Matrix Rank

• Used in: Q26

• Concept: The number of non-zero rows in row-echelon form.

• Rank of Matrix

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11. Matrix Order & Properties

• Used in: Q11

• Concept: Order = Rows × Columns

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12. Expressing a Matrix as Symmetric + Skew-Symmetric

• Used in: Q13, Q18

• Concept: A = ½(A + Aᵗ) + ½(A - Aᵗ)

• Matrix = Symmetric + Skew Symmetric | Shortcut

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13. Conditions for Unique or Infinite Solutions

• Used in: Q24

• Concept: Based on rank and consistency of augmented matrix.

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