Let T be a linear operator on a finite-dimensional vector space V, and let W1,W2, . . . ,Wk be T-invariant subspaces of V such that V = W1⊕W2⊕·· ·⊕Wk. Prove that det(T) = det(TW1) det(TW2)  · · det(TWk).

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.