QLDSpecialist MathematicsQuick questions

Unit 3: Mathematical induction, and further vectors, matrices and complex numbers

Quick questions on Systems of linear equations and larger matrices in QCE Specialist Mathematics Unit 3

Q: What is matrix form of a system?

A system such as $aligned a_1 x + b_1 y + c_1 z &= d_1\\ a_2 x + b_2 y + c_2 z &= d_2\\ a_3 x + b_3 y + c_3 z &= d_3 alignedis written compactly asA\mathbf{x} = \mathbf{b}, whereAis the3\times 3matrix of coefficients,\mathbf{x} = (x, y, z)^{\mathsf T}and\mathbf{b} = (d_1, d_2, d_3)^{\mathsf T}$.

Q: What is solve by elimination?

Subtract the first from the second: x - 2y = -3. Add the first and third (eliminating z): 2x + 3y = 8. From x = 2y - 3, substitute: 2(2y - 3) + 3y = 8, so 7y = 14, giving y = 2.

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is matrix form of a system?

Show answer

A system such as $

\begin{aligned} a_1 x + b_1 y + c_1 z &= d_1\\ a_2 x + b_2 y + c_2 z &= d_2\\ a_3 x + b_3 y + c_3 z &= d_3 \end{aligned}

is written compactly as

A\mathbf{x} = \mathbf{b}

, where

is the

3\times 3

matrix of coefficients,

\mathbf{x} = (x, y, z)^{\mathsf T}

and

\mathbf{b} = (d_1, d_2, d_3)^{\mathsf T}$.

What is solve by elimination?

Show answer

Subtract the first from the second:

x - 2y = -3

. Add the first and third (eliminating

z

2x + 3y = 8

. From

x = 2y - 3

, substitute:

2(2y - 3) + 3y = 8

, so

7y = 14

, giving

y = 2

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