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$\\var{a}+\\var{b}$                                                                          

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$\\Bigg($[[0]][[1]]$\\Bigg)$
[[2]][[3]]
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$\\var{p}\\var{c}-\\var{q}\\var{d}$

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$\\Bigg($[[0]][[1]]$\\Bigg)$
[[2]][[3]]
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(a)

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$\\var{a}+\\var{b}=\\var{u}$

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Just add corresponding elements together.

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(b)

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$\\var{p}\\var{c}-\\var{q}\\var{d}$

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Multiply each element of the first matrix by $\\var{p}$...

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$\\var{p}\\var{c}=\\var{pc}$

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...and multiply each element of the second matrix by $\\var{q}$.

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$\\var{q}\\var{d}=\\var{qd}$

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Finally, subtract corresponding elements

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$\\var{p}\\var{c}-\\var{q}\\var{d}=\\var{pc}-\\var{qd}=\\var{v}$

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For more explanation, look for relevant resources in the 'Matrices' section on our Maths Study Skills page.

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Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

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(Last three parts of original question removed.)

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