Scalar Multiple (Edexcel A-Level Further Mathematics): Quizzes

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Scalar Multiple
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What is a scalar in the context of matrices?

A real number that multiplies each element

When a matrix is multiplied by a scalar, what happens to each entry?

Every entry is scaled by the same factor

Calculate 2(310−2)2\begin{pmatrix} 3 & 1 \\ 0 & -2 \end{pmatrix}

(620−4)\begin{pmatrix} 6 & 2 \\ 0 & -4 \end{pmatrix}

What is −3(1−240)-3\begin{pmatrix} 1 & -2 \\ 4 & 0 \end{pmatrix}?

(−36−120)\begin{pmatrix} -3 & 6 \\ -12 & 0 \end{pmatrix}

Which property shows associativity of scalar multiplication with matrices?

λ(A×B)=(λA)×B\lambda(A \times B) = (\lambda A) \times B

Can scalar multiplication be performed before or after matrix multiplication?

Yes, without affecting the result

Does multiplying a matrix by a scalar change its size?

No, the scalar doesn't change matrix size

If A=(1203)A=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix} and B=(2011)B=\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}, does 2(AB)=(2A)B2(AB)=(2A)B?

Yes, they are equal

A common mistake is forgetting to apply the scalar to which elements?

All elements of the matrix

When is matrix multiplication A×BA \times B defined?

When the inner dimensions match

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