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Exercise 14Linear algebra › Matrices and linear systemsHigh schoolAdded 3 Nov 2026

Matrix addition and scalar multiplication

#matrix operations#addition#scalar multiplication

Statement

Let
A=(1234),B=(0−125).A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \qquad B = \begin{pmatrix} 0 & -1 \\ 2 & 5 \end{pmatrix}.
Compute A+BA+B, 3A3A, and 2A−3B2A - 3B.

Hint

Add matrices entry by entry; multiply each entry by the scalar.

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Solution

Sum.
A+B=(1+02−13+24+5)=(1159).A+B = \begin{pmatrix} 1+0 & 2-1 \\ 3+2 & 4+5 \end{pmatrix} = \begin{pmatrix} 1 & 1 \\ 5 & 9 \end{pmatrix}.

Scalar multiple.
3A=(36912).3A = \begin{pmatrix} 3 & 6 \\ 9 & 12 \end{pmatrix}.

Linear combination.
2A=(2468),3B=(0−3615),2A = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix}, \qquad 3B = \begin{pmatrix} 0 & -3 \\ 6 & 15 \end{pmatrix},
so
2A−3B=(270−7).2A - 3B = \begin{pmatrix} 2 & 7 \\ 0 & -7 \end{pmatrix}.