3.2 Matrix operations (Exercises)

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To compute the sum of two matrices.

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To compute $c_{1}A+c_{2}B$.

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To compute $c_{1}A+c_{2}B$.

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To solve equations involving sum and transpose.

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True/False questions involving sum and transpose.

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To compute a product $AB$.

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To compute a product $AB$.

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To compute a product $AB$.

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To compute a product $AB$.

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To compute several matrix products.

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To compute $\text{vect}{u}^T\text{vect}v$ and $\text{vect}u\text{vect}{v}^T$.

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To find $k$ for which $AB=BA$.

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To find $k$ for which $AB=BA$.

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To find two products $A{D}_1$ and $D_{2}A$.

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To find a high power of a special matrix.

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To find a high power of a special matrix.

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Is the zero matrix a diagonal matrix?

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To explain why a certain product does not exist.

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To find a $2\times 2$ matrix $A$ for which $A^2=-I$.

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To show that $(cA{)}^T=c{A}^T$.

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'To show: $A^{T}A=D⟺A$ has orthogonal columns.'

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To find the size of $C$ if $AC=B$.

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Number of columns of $C$ if $AC=B$.

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To find the number of rows of $B$ if $BC$ is an $m\times n$-matrix.

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Finding $E$ such that $EA=M$ (or $AE=M$).

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A bit like the previous one 'by inspection'.

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Two True/False questions about products and symmmetric matrices.