// Numbas version: finer_feedback_settings {"name": "Matrix Addition and Subtraction", "metadata": {"description": "

This exam gives an overview of skills studnets require to be able to add and subtract matrices.

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Addition of Matrices

\n

For each of the following matrices, carry out the addition

", "advice": "

Addition is achieved by adding corresponding elements:

\n

\n

Using this technique gives us:

\n

a)

\n

$A + B = \\var{A} + \\var{A2} = \\var{ad1}$

\n

\n

b)

\n

$C + D = \\var{B} + \\var{B2} = \\var{ad2}$

\n

\n

c)

\n

$E + F = \\var{C} + \\var{C2} = \\var{ad3}$

\n

\n

d)

\n

$G + H = \\var{D} + \\var{D2} = \\var{ad4}$

\n

\n

e)

\n

$I + J = \\var{EE} + \\var{EE2} = \\var{ad5}$

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3#1)", "description": "", "templateType": "randrange", "can_override": false}, "m5": {"name": "m5", "group": "E", "definition": "random(2 .. 4#1)", "description": "", "templateType": "randrange", "can_override": false}, "EE": {"name": "EE", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything", "can_override": false}, "e1": {"name": "e1", "group": "A", "definition": "A[n1-1][m1-1]", "description": "", "templateType": "anything", "can_override": false}, "E2": {"name": "E2", "group": "B", "definition": "b[n2-1][m2-1]", "description": "", "templateType": "anything", "can_override": false}, "trC": {"name": "trC", "group": "C", "definition": "(C[0][0])+(C[1][1])+(C[2][2])+(C[3][3])+(C[4][4])", "description": "", "templateType": "anything", "can_override": false}, "A2": {"name": "A2", "group": "A", "definition": "transpose(matrix(repeat(repeat(random(0..9),n1),m1)))", "description": "", "templateType": "anything", "can_override": false}, "B2": {"name": "B2", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything", "can_override": false}, "D2": {"name": "D2", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything", "can_override": false}, "EE2": {"name": "EE2", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything", "can_override": false}, "ad1": {"name": "ad1", "group": "Ungrouped variables", "definition": "{A}+{A2}", "description": "", "templateType": "anything", "can_override": false}, "ad2": {"name": "ad2", "group": "Ungrouped variables", "definition": "{B}+{B2}", "description": "", "templateType": "anything", "can_override": false}, "ad3": {"name": "ad3", "group": "Ungrouped variables", "definition": "{C}+{C2}", "description": "", "templateType": "anything", "can_override": false}, "ad4": {"name": "ad4", "group": "Ungrouped variables", "definition": "{D}+{D2}", "description": "", "templateType": "anything", "can_override": false}, "ad5": {"name": "ad5", "group": "Ungrouped variables", "definition": "{EE}+{EE2}", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ad1", "ad2", "ad3", "ad4", "ad5"], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A", "e1", "A2"]}, {"name": "B", "variables": ["n2", "m2", "B", "E2", "B2"]}, {"name": "C", "variables": ["n3", "m3", "C", "trC", "C2"]}, {"name": "D", "variables": ["n4", "m4", "D", "D2"]}, {"name": "E", "variables": ["n5", "m5", "EE", "EE2"]}], "functions": {"calculateTrace": {"parameters": [], "type": "number", 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Let:

\n

$$
A=\\var{A}, B=\\var{A2}
$$

Calculate $A+B$:

\n

$A+B=$ [[0]]

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Let:

\n

$$
C=\\var{B}, D=\\var{B2}
$$

\n

Calculate $C+D$:

\n

$C+D=$ [[0]]

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Let

\n

$$
E=\\var{C}, F=\\var{C2}
$$

\n

Calculate $E+F$:

\n

$E+F=$ [[0]]

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Let:

\n

$$
G=\\var{D}, H=\\var{D2}
$$

\n

Calculate $G+H$:

\n

 $G+H=$ [[0]]

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Let:

\n

$$
I=\\var{EE}, J=\\var{EE2}
$$

\n

Calculate $I+J$:

\n

$I+J=$ [[0]]

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Subtraction of Matrices

\n

For each of the following matrices, carry out the subtraction

", "advice": "

Subtraction is achieved by subtracting corresponding elements:

\n

\n

Using this technique gives us:

\n

a)

\n

$$
\\begin{aligned}
A - B &= \\var{A} - \\var{A2} \\\\
&= \\var{ad1}
\\end{aligned}
$$

\n

b)

\n

$$
\\begin{aligned}
C - D &= \\var{B} - \\var{B2} \\\\
&= \\var{ad2}
\\end{aligned}
$$

\n

c)

\n

$$
\\begin{aligned}
E - F &= \\var{C} - \\var{C2} \\\\
&= \\var{ad3}
\\end{aligned}
$$

\n

d)

\n

$$
\\begin{aligned}
G - H &= \\var{D} - \\var{D2} \\\\
&= \\var{ad4}
\\end{aligned}
$$

\n

e)

\n

$$
\\begin{aligned}
I - J &= \\var{EE} - \\var{EE2} \\\\
&= \\var{ad5}
\\end{aligned}
$$

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"can_override": false}, "B2": {"name": "B2", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything", "can_override": false}, "C2": {"name": "C2", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything", "can_override": false}, "D2": {"name": "D2", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything", "can_override": false}, "EE2": {"name": "EE2", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything", "can_override": false}, "ad1": {"name": "ad1", "group": "Ungrouped variables", "definition": "{A}-{A2}", "description": "", "templateType": "anything", "can_override": false}, "ad2": {"name": "ad2", "group": "Ungrouped variables", "definition": "{B}-{B2}", "description": "", "templateType": "anything", "can_override": false}, "ad3": {"name": "ad3", "group": "Ungrouped variables", "definition": "{C}-{C2}", "description": "", "templateType": "anything", "can_override": false}, "ad4": {"name": "ad4", "group": "Ungrouped variables", "definition": "{D}-{D2}", "description": "", "templateType": "anything", "can_override": false}, "ad5": {"name": "ad5", "group": "Ungrouped variables", "definition": "{EE}-{EE2}", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ad1", "ad2", "ad3", "ad4", "ad5"], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A", "e1", "A2"]}, {"name": "B", "variables": ["n2", "m2", "B", "E2", "B2"]}, {"name": "C", "variables": ["n3", "m3", "C", "trC", "C2"]}, {"name": "D", "variables": ["n4", "m4", "D", "D2"]}, {"name": "E", "variables": ["n5", "m5", "EE", "EE2"]}], "functions": {"calculateTrace": {"parameters": [], "type": "number", 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Let:

\n

$$
A=\\var{A}, B=\\var{A2}
$$

\n

Calculate $A-B$:

\n

$A-B=$ [[0]]

\n

\n

\n

\n

\n

                    

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Let:

\n

$$
C=\\var{B}, D=\\var{B2}
$$

\n

Calculate $C-D$: 

\n

$C-D=$ [[0]]

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Let:

\n

$$
E=\\var{C}, F=\\var{C2}
$$

\n

Calculate $E-F$:

\n

$E-F=$ [[0]]

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Let:

\n

$$
G=\\var{D}, H=\\var{D2}
$$

\n

Calculate $G-H$:

\n

$G-H=$ [[0]]

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Let:

\n

$$
I=\\var{EE}, J=\\var{EE2}
$$

\n

Calculate $I-J$:

\n

$I-J=$ [[0]]

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