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Exercise 5

Avg difficulty 3.0

Find the dimension of the vector space of matrices

(abcd)\begin{pmatrix}a&b\\ c&d\end{pmatrix}

subject to each condition.

  • a,b,c,d∈Ra,b,c,d\in\mathbb{R}

  • a−b+2c=0a-b+2c=0 and d∈Rd\in\mathbb{R}

  • a+b+c=0a+b+c=0, a+b−c=0a+b-c=0, and d∈Rd\in\mathbb{R}

Hefferon, Linear Algebra, Vector Spaces, Dimension, Exercise 5

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.