A First Course in Linear Algebra · Problem M21

Determinants — Robert Beezer

Mathematics — Linear Algebra · dimension-subspace

Problem

A 2×22 \times 2 matrix BB is upper triangular if [B]21=0[B]_{21} = 0. Let UT2UT_2 be the set of all 2×22 \times 2 upper triangular matrices. Then UT2UT_2 is a subspace of the vector space of all 2×22 \times 2 matrices, M22M_{22} (you may assume this). Determine the dimension of UT2UT_2 providing all of the necessary justifications for your answer.

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