Prove that if A is an n × p matrix and D = diag ( d 1 , d 2 , … , d n ) , then D A is the matrix obtained by multiplying the i − th row vector of A by d i , where 1 ≤ i ≤ n .
Prove that if A is an n × p matrix and D = diag ( d 1 , d 2 , … , d n ) , then D A is the matrix obtained by multiplying the i − th row vector of A by d i , where 1 ≤ i ≤ n .
Solution Summary: The author explains that the matrix A is an ntimes p matrix and D=diag(d_1,
Prove that if
A
is an
n
×
p
matrix and
D
=
diag
(
d
1
,
d
2
,
…
,
d
n
)
, then
D
A
is the matrix obtained by multiplying the
i
−
th
row vector of
A
by
d
i
, where
1
≤
i
≤
n
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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