Answer:
Step-by-step explanation:
An eigenvalue of n × n is a function of a scalar considering that there is a solution (i.e. nontrivial) to an eigenvector x of Ax =
Suppose the matrix
Thus, the equation of the determinant (A - 1) = 0
This implies that:
Hence, the eigenvalues of the equation are
Also, the eigenvalues can be said to be complex numbers.
We're told (and we can confirm) that , so
is a linear combination of the other two vectors.
This means <em>H</em> is sufficiently spanned by ; no need for the third vector.
But this also means we can write either as a linear combination of
, and
as a lin. com. of
. So any set of these three vectors taken two at a time will span the subspace <em>H</em>. Hence all of b, c, and d are acceptable.
The volume of one die is the edge to the power of 3:
The total volume is five times the above volume:
Answer: