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Date May Example question Marks available 2 Reference code EXM.1.AHL.TZ0.43
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Solve Question number 43 Adapted from N/A

Question

Find the values of aa and bb given that the matrix A=(a46857534)A=a46857534 is the inverse of the matrix B=(1223b1113)B=1223b1113.

[2]
a.

For the values of aa and bb found in part (a), solve the system of linear equations

x+2y2z=53x+by+z=0x+y3z=a1.x+2y2z=53x+by+z=0x+y3z=a1.

[2]
b.

Markscheme

AB = I

(AB)11 = 1 ⇒ aa – 12 + 6 = 1,    giving aa = 7          (A1) (C1)

(AB)22 = 1 ⇒ –16 + 5bb + 7 = 1,    giving bb = 2          (A1) (C1)

[2 marks]

a.

the system is BX=(506)BX=506 where X=(xyz)X=xyz.

Then, X=A(506)=(746857534)(506).X=A506=746857534506.          (M1)

Thus x=1x=1y=2y=2z=1z=1          (A1) (C2)

[2 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 1—Number and algebra » AHL 1.14—Introduction to matrices
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Topic 1—Number and algebra

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