All Linear Algebra Resources
Example Questions
Example Question #191 : Linear Algebra
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Correct answer:
Explanation:
Example Question #14 : The Trace
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Explanation:
Example Question #114 : Operations And Properties
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Example Question #14 : The Trace
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Example Question #192 : Linear Algebra
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Example Question #15 : The Trace
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Correct answer:
Explanation:
Example Question #193 : Linear Algebra
,
where
is a complex number. The trace of is 50.Evaluate
.
Possible Answers:
Correct answer:
Explanation:
is a diagonal matrix - its only nonzero elements are on the main diagonal, from upper left to lower right - so its square can be taken by simply squaring the diagonal elements. Since
it follows that
The trace of a matrix is equal to the sum of the elements in its main diagonal, so the trace of
is
Since the trace is given to be 50, set this equal to 50 and solve for
:
Example Question #15 : The Trace
Evaluate
so that the trace of is equal to 10.
Possible Answers:
The trace of
cannot be 10 regardless of the value of
Correct answer:
Explanation:
The trace of a matrix is equal to the sum of the elements in its main diagonal - the elements going from upper left to lower right. Therefore,
Since the trace of
is equal to 10, set equal to this and solve for :
Example Question #21 : The Trace
where
is a real number.Which expression is equal to the trace of
?
Possible Answers:
Correct answer:
Explanation:
The trace of a matrix is equal to the sum of the elements in its main diagonal - the elements going from upper left to lower right. Therefore,
Example Question #22 : The Trace
,
Give the trace of
.
Possible Answers:
Correct answer:
Explanation:
and are both diagonal matrices - their only nonzero elements are on their main diagonals, from upper left to lower right - so their product can be found by multiplying their corresponding diagonal elements:
The trace of a matrix is equal to the sum of the elements in its main diagonal, so the trace of
is
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