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Addition

Adding same-size matrices entry by entry, and using only the addition axioms to prove cancellation facts such as A + B = 0 forcing B = -A.

Matrix Theory and Linear Algebra, Addition

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3 exercises

Exercise 4.2.3

Let $A=\left[\begin{array}{rrr}1&2&-1\\ -1&4&0\\ \end{array}\right]$ and $B=\left[\begin{array}{rrr}0&3&0\\ 1&-1&1\\ \end{array}\right]$ .

Find a matrix $X$ such that $(A+X)-(B+0)=B+A$ . Hint: first use the properties of matrix addition to simplify the equation and solve for $X$ .

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Exercise 4.2.4

Using only the properties given in Proposition 4.15, show that if $A+B=0$ , then $B=-A$ .

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Exercise 4.2.5

Using only the properties given in Proposition 4.15, show $A+B=A$ implies $B=0$ .

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.