A vector space
is a subspace of a vector space
if
is non-empty,- for any two vectors
we have
, and - for any scalar
and
we have
.
It's easy to show the first condition is met by all the sets in parts (a-g).
(a) is a subspace of
because adding any 2x2 diagonal matrices together, or multiplying one by some scalar, gives another diagonal matrix.
(b) and (c) are also subspaces for the same reasons.
(d) is not a subspace because
because this set of matrices does not contain the zero matrix.
(e), however, is a subspace. Any linear combination of matrices in this set always yields a matrix with 0 in row 1, column 1 entry.
(f) is a subspace. A symmetric matrix is one of the form

Adding two symmetric matrices gives another symmetric matrix:

(g) is not a subspace. Consider the matrices

Both matrices have determinant 0, but their sum is the identity matrix with determinant 1.
The product of multiplication of 16 × 9 gives us; 144
<h3>Multiplication</h3>
We want to find the product of 16 and 9.
Now, to solve this we can use a little illustration for example if I have a basket of oranges and I want to given 9 people each 16 oranges, it means that the total number of oranges I will give out is; 16 × 9 = 144
Thus, our question answer is 16 × 9 = 144
Read more on multiplication at; brainly.com/question/2475734
Answer:
X=1/2
Step-by-step explanation:
-2x1/2=-1
-2x1=-2
-1+-2=-3