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03/13/2024
➤Module-I System of Linear Equations:-
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➤Symmetric Matrix
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➤Skew-Symmetric Matrix
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➤Diagonal Matrix
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➤Upper Triangular Matrix
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➤Lower Triangular Matrix
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➤Orthogonal Matrix
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➤Hermitian Matrix
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➤Non-Hermitian Matrix
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➤Nilpotent Matrix
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➤Idempotent Matrix
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➤Sub Matrix
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➤Minor
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➤Rank of Matrix
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Q. Find the Rank of the following matrices.
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➤Rank of Matrix in Row-Echelon Form?
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➤Elementary Row Operation
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➤Echelon Form of Matrix:
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Q. Find the condition on p,q, and r for which this matrix has:
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⭐System of Linear Equations➤Augmented Matrix
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➤Augmented Matrix Properties
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➤{{c1::Number of zero rows}} in Echelon form of Matrix = {{c2::RANK}}
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⭐Homogeneos Equations❖ Types, Names and Conditions
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Q. Consider the Augmented Matrix and try to convert it into echelon form.
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Q. Consider the Augmented Matrix and try to convert it into echelon form.
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➤Using Row-Echelon Method:
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➤Write some important properties of Vector Space.
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Q. What do you mean by Vector Space?
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Q, Write Vector Addition Properties of Vector Space.
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Q, Write Vector Multiplication Properties of Vector Space.
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➤What do you mean by Subspace?
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➤Theorem - 01
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⭐SUBSPACE➤Theorem - 02
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⭐SUBSPACE➤Theorem-03
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⭐SUBSPACE➤Theorem-04
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⭐SUBSPACE➤Theorem-?
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⭐SUBSPACE➤Sum of Two Subspaces
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⭐SUBSPACE➤Direct Sum➤Definition
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⭐SUBSPACE➤Direct Sum➤Definition➤Theorem
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⭐SUBSPACE➤Linear Combination➤Definition
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⭐SUBSPACE➤Linear Combination
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⭐SUBSPACE➤Linear Combination
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⭐SUBSPACE➤Linear Combination
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⭐SUBSPACE➤Linear Combination
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent➤Complex Numbers = {{c1::Row-Wise}}➤Real Numbers = {{c2::Column-Wise}}
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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⭐SUBSPACE➤Linear Combination➤Linearly Independent or Linearly Dependent
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