Let V be the set of 2 × 2 matrices with entries from R, that is, V ={ [ a b c d ] | a, b, c, d ∈ R } equipped with operations: [ a b c d ] + [ x y w z ] = [ a + x b + y c + w d + z ] and λ [ a b c d ] = [ λa λb λc λd ] where a, b, c, d, x, y, w, z ∈ R and λ ∈ R. Show that V is a vector space over R with these operations
Let V be the set of 2 × 2 matrices with entries from R, that is, V ={ [ a b c d ] | a, b, c, d ∈ R } equipped with operations: [ a b c d ] + [ x y w z ] = [ a + x b + y c + w d + z ] and λ [ a b c d ] = [ λa λb λc λd ] where a, b, c, d, x, y, w, z ∈ R and λ ∈ R. Show that V is a vector space over R with these operations
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 76E
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Let V be the set of 2 × 2 matrices with entries from R, that is,
V ={ [ a b
c d ] | a, b, c, d ∈ R }
equipped with operations:
[ a b
c d ]
+
[ x y
w z ]
=
[ a + x b + y
c + w d + z ]
and
λ [ a b
c d ]
=
[ λa λb
λc λd ]
where a, b, c, d, x, y, w, z ∈ R and λ ∈ R.
Show that V is a
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