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Example Question #7 :Symmetric Matrices
Example Question #8 :Symmetric Matrices
Example Question #71 :Operations And Properties
Example Question #10 :Symmetric Matrices
Example Question #11 :Symmetric Matrices
Example Question #11 :Symmetric Matrices
Example Question #151 :Linear Algebra
Example Question #14 :Symmetric Matrices
True or false:is an example of a skew-symmetric matrix.
False
True
False
A square matrixis defined to be skew-symmetric if its transpose- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Interchanging rows and columns, we see that if
,
then
.
can be determined by changing each element into its additive inverse:
, since not every element in corresponding positions is equal; in particular, the three elements in the main diagonal differ.is not a skew-symmetric matrix.
Example Question #15 :Symmetric Matrices
True or false:is an example of a skew-symmetric matrix.
False
True
True
A square matrixis defined to be skew-symmetric if its transpose- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Interchanging rows and columns, we see that if
,
then
.
We see that each element ofis the additive inverse of the corresponding element in, so, andis skew-symmetric.
Example Question #16 :Symmetric Matrices
is a three-by-three nonsingular skew-symmetric matrix
Then which of the followingmustbe equal to?
A square matrixis defined to be skew-symmetric if its transpose- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Therefore, by substitution,
必须等于相反of the three-by-three identity matrix, which is.
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