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GCSEFurther MathsAQAExam Questions5. Matrix TransformationsMatrix Multiplication

Matrix Multiplication (AQA GCSE Further Maths)

Exam Questions

49 mins13 questions
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1
Sme Calculator1 mark

bold P equals open parentheses table row 5 0 row cell negative 2 end cell 3 end table close parentheses and bold Q equals open parentheses table row 2 row 4 end table close parentheses

Work out bold PQ.

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2
Sme Calculator3 marks

a open parentheses table row 3 row 5 end table close parentheses equals 4 open parentheses table row cell 2 a plus 3 end cell row b end table close parentheses

Work out the values of a and b.

a space equals.............. space b space equals..............

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3
Sme Calculator2 marks

open parentheses table row m cell negative 1 end cell row 1 1 end table close parentheses open parentheses table row 2 2 row cell negative 2 end cell cell negative 1 end cell end table close parentheses equals bold I where bold I is the identity matrix.

Work out the value of m.

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4
Sme Calculator2 marks

bold A equals open parentheses table row 2 4 row 3 cell negative 1 end cell end table close parentheses space and bold B equals open parentheses table row cell negative 2 end cell 6 row 2 1 end table close parentheses

Work out bold AB.

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5
Sme Calculator3 marks

4 open parentheses table row cell 1 minus 2 a end cell row a end table close parentheses equals open parentheses table row b row 12 end table close parentheses

Work out the values of a and b.

a equals space................. space space b space equals space................

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1a
Sme Calculator3 marks

bold A equals open parentheses table row 4 cell negative 1 end cell row cell negative 7 end cell 2 end table close parentheses              bold B equals open parentheses table row s row cell negative 5 end cell end table close parentheses               bold C equals open parentheses table row cell negative 1 end cell row t end table close parentheses              bold D equals open parentheses table row 2 1 row 7 u end table close parentheses

s comma space t and u are constants.

bold AB equals bold C

Work out the values of s and t.

s equals.....................................

t equals.....................................

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1b
Sme Calculator1 mark

bold AD equals bold I

Work out the value of u.

u space equals..........................

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2
Sme Calculator3 marks

open parentheses table row 1 k row cell negative 3 space end cell 0 end table close parentheses open parentheses table row 0 cell negative k end cell row 3 1 end table close parentheses equals 12 bold I where bold I is the identity matrix.

Find the value of k.

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3
Sme Calculator4 marks

open parentheses table row 2 1 row 0 3 end table close parentheses open parentheses table row a b row 0 cell 0.4 end cell end table close parentheses equals k bold I where k is a constant and bold I is the identity matrix.

Work out the values of a and b.

a space equals................. space b space equals.................   

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4
Sme Calculator4 marks

bold M equals open parentheses table row 4 cell negative 5 end cell row cell negative 1 end cell 2 end table close parentheses and bold P equals open parentheses table row 7 a row b c end table close parentheses

bold M squared equals k bold P where bold M squared equals bold MM and k is an integer.

Find the values of a, b and c.

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5
Sme Calculator6 marks

bold A equals open parentheses table row 1 3 row cell negative 2 end cell 0 end table close parentheses and bold B equals open parentheses table row p row q end table close parentheses

bold C equals bold AB

bold D equals bold AC

If bold D equals open parentheses table row cell k q end cell row 0 end table close parentheses where k is an integer, find the value of k.

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1
Sme Calculator5 marks

bold A equals open parentheses table row 1 4 row 5 2 end table close parentheses and bold B equals open parentheses table row cell negative 4 end cell p row q cell negative 2 end cell end table close parentheses where p and q are integers.

If bold AB equals bold BA, find the values of p and q.

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2
Sme Calculator6 marks

open parentheses table row x cell 5 minus x squared end cell row cell negative 3 space end cell cell negative 1 end cell end table close parentheses open parentheses table row cell x minus 2 space end cell 1 row cell 2 space space space end cell 1 end table close parentheses equals open parentheses table row 2 a row b c end table close parentheses where x is negative and a, b and c are integers.

Find the values of a, b and c.

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3
Sme Calculator6 marks

open parentheses table row cell 1 space space end cell cell negative 4 end cell row cell x space space end cell cell x plus y end cell end table close parentheses open parentheses table row x row y end table close parentheses equals 3 open parentheses table row cell negative 2 end cell row 1 end table close parentheses

Find the possible values of x and y.

Do not use trial and improvement.

You must show your working.

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