Matrix arithmetic

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Frank Doheny

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8 years, 1 month ago

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Name	Status	Author	Last Modified
Matrix arithmetic	Ready to use	Frank Doheny	14/03/2018 21:06
Mark's copy of Matrix arithmetic	draft	Mark Hodds	07/09/2017 14:58
John's copy of Matrix arithmetic	draft	John Steele	13/05/2019 03:57
Maria's copy of John's copy of Matrix arithmetic	draft	Maria Aneiros	24/05/2019 00:01
Josh's copy of John's copy of Matrix arithmetic	draft	Josh Lim	21/06/2019 15:33
L1 - Matrix arithmetic combined	Ready to use	Timur Zaripov	17/06/2022 09:37

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Question statement

Given the matrix:

$A=\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a11	integer	10
a12	integer	10
a21	integer	2
a22	integer	16
k1	integer	7
k2	integer	10
b11	number	200
b12	integer	66
b21	integer	330
b22	number	398

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Generated value: `integer`

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Parts

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1. Gap Matrix entry
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Evaluate the following expression:

$\left(A^2+\var{k1}A+\var{k2}I\right)^t$ = Unnamed gap

Advice

$A=\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}$

$A^2=\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}$

Remember multiplication of matrices is carried out by multiplying the rows of the first matrix by the columns of the second matrix.

$A^2=\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}\begin{pmatrix} \var{a11}& \var{a12}\\ \var{a21}&\var{a22}\end{pmatrix}=\begin{pmatrix}\var{a11}*\var{a11}+\var{a12}*\var{a21}&\var{a11}*\var{a12}+\var{a12}*\var{a22}\\ \var{a21}*\var{a11}+\var{a22}*\var{a21}&\var{a21}*\var{a12}+\var{a22}*\var{a22}\end{pmatrix}$

$A^2=\begin{pmatrix}\simplify{{a11}*{a11}+{a12}*{a21}}&\simplify{{a11}*{a12}+{a12}*{a22}}\\ \simplify{{a21}*{a11}+{a22}*{a21}}&\simplify{{a21}*{a12}+{a22}*{a22}}\end{pmatrix}$

$\var{k1}A=\begin{pmatrix} \var{k1}*\var{a11}& \var{k1}*\var{a12}\\ \var{k1}*\var{a21}&\var{k1}*\var{a22}\end{pmatrix}=\begin{pmatrix} \simplify{{k1}*{a11}}& \simplify{{k1}*{a12}}\\ \simplify{{k1}*{a21}}&\simplify{{k1}*{a22}}\end{pmatrix}$

$\left(A^2+\var{k1}A+\var{k2}I\right)^t=\left(\begin{pmatrix}\simplify{{a11}*{a11}+{a12}*{a21}}&\simplify{{a11}*{a12}+{a12}*{a22}}\\ \simplify{{a21}*{a11}+{a22}*{a21}}&\simplify{{a21}*{a12}+{a22}*{a22}}\end{pmatrix}+\begin{pmatrix} \simplify{{k1}*{a11}}& \simplify{{k1}*{a12}}\\ \simplify{{k1}*{a21}}&\simplify{{k1}*{a22}}\end{pmatrix}+\begin{pmatrix} \var{k2}&0\\0&\var{k2}\end{pmatrix}\right)^t$

$\left(A^2+\var{k1}A+\var{k2}I\right)^t=\begin{pmatrix}\simplify{{a11}*{a11}+{a12}*{a21}+{k1}{a11}+{k2}}&\simplify{{a11}*{a12}+{a12}*{a22}+{k1}*{a12}}\\ \simplify{{a21}*{a11}+{a22}*{a21}+{k1}*{a21}}&\simplify{{a21}*{a12}+{a22}*{a22}+{k1}*{a22}+{k2}}\end{pmatrix}^t$

$\left(A^2+\var{k1}A+\var{k2}I\right)^t=\begin{pmatrix}\simplify{{a11}*{a11}+{a12}*{a21}+{k1}{a11}+{k2}}&\simplify{{a21}*{a11}+{a22}*{a21}+{k1}*{a21}}\\ \simplify{{a11}*{a12}+{a12}*{a22}+{k1}*{a12}}&\simplify{{a21}*{a12}+{a22}*{a22}+{k1}*{a22}+{k2}}\end{pmatrix}$

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This question is used in the following exams:

Matrix Algebra 1 by Sara Lombardo in Sara's workspace.
Exam2 by Sara Lombardo in Sara's workspace.
Matrix arithmetic by Frank Doheny in Matrices.
MATH1902 Quiz 3 Linear Algebra by Blathnaid Sheridan in Blathnaid's workspace.

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Frank Doheny 8 years, 1 month ago

Frank Doheny 8 years, 1 month ago

Frank Doheny 8 years, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Matrix arithmetic

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 8 years, 1 month ago

Frank Doheny 8 years, 1 month ago

Frank Doheny 8 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`