In linear algebra, the rank of a matrix
A
A is the dimension of the vector space generated (or spanned) by its columns.[1] This corresponds to the maximal number of linearly independent columns of
A
A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[2] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by
A
A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
The rank is commonly denoted by
rank
(
A
)
{\displaystyle \operatorname {rank} (A)} or
rk
(
A
)
{\displaystyle \operatorname {rk} (A)}; sometimes the parentheses are not written, as in
rank
A
{\displaystyle \operatorname {rank} A}.
Answer:
Pair 1.
Step-by-step explanation:
On pair 1, shape A can go into shape B with a rotation.
Pair 2 would be a translation.
Pair 3 would be a reflection across the x-axis.
Pair 4 would be a reflection across the y-axis.
Answer:
A number and its additive inverse are always the same distance from zero, and so they have the same absolute value.
Step-by-step explanation:
Hope this helps!!
Answer:
A
Step-by-step explanation:
