Mathematics">
Guia 2 Matrices Operaciones.
Guia 2 Matrices Operaciones.
Guia 2 Matrices Operaciones.
1
𝒂. 𝐴 + 𝐶 𝑡 = 𝒃. 𝐴 × 𝐵 = 𝒄. 2𝐶 × 𝐵 + 𝐴𝑡 = 𝒅. 𝐵𝑡 − 𝐵 =
2
𝑎. 𝑋 + 𝐴 = 3𝑋 + 2𝐵
4𝑋 + 3𝑌 = 𝐴
𝑏. { .
2𝑋 + 𝑌 = 𝐵
3. Calcula la inversa de las siguientes matrices:
1 3 6 1 2 0 1 −2 2 2
𝑨 = (2 1 7) 𝑩 = (2 −1 2 ) 𝑪 = (0 4 −2 1 )
1 −2 4 0
1 −2 −1 3𝑋3 0 5 −2 3𝑋3
1 −2 2 2 4𝑋4
0 𝑎 0 1 0 3 1
0 𝑎 𝑏
𝑫 = (𝑏 𝑐 𝑑) 𝑬 = (𝑎 0 𝑐) 𝑭=( 2 2 6 0)
−1 0 −3 1
0 𝑒 0 3𝑋3 𝑏 𝑐 0 3𝑋3 4 1 12 0 4𝑋4
𝟏 𝟐
5. Si la matriz: 𝑨=( ) satisface la igualdad 𝑨𝟐 + 𝒙 ∙ 𝑨 + 𝒚 ∙ 𝑰 = 𝟎, halla los valores
−𝟑 𝟒
0 5 −4
3𝑋 − 2𝑌 = ( 5 9 0)
15
. −4 4
7 1 2
2𝑋 − 𝑌 = (−6 6 7)
{ 10 −5 −2
1 1 0 −1 2 1 1 2 −5
𝑨 = (1 0 1) 𝑩=( 1 0 2) 𝑪=( 2 3 −8)
0 1 0 3𝑋3 2 1 −1 3𝑋3 −1 −1 5 3𝑋3
1 −2 2 2 2 1 −3 2
−3 5 8
𝑫 = ( 2 4 6) 𝑬 = (0 2 −2 1) 𝑭=( −4 2 4 −1)
1 −2 4 0 −2 1 1 4
−1 7 4 3𝑋3 1 −1 2 2 4𝑋4 1 −2 −1 4 4𝑋4
0 4 3
0 1 −2 3
𝑨=( ) 𝑩=( ) 𝑪 = (0 1 6)
4 8 2𝑋2 5 −9 2𝑋2
2 7 5 3𝑋3
3 4 0 1 0 0 1 1 0 0
𝑫 = (1 0 −1 −2 0)
5 6) 𝑬=( 0 𝑖 2𝑖 ) 𝑭=(
0 0 1 −1
2 1 0 3𝑋3 1−𝑖 0 1 + 𝑖 3𝑋3
0 0 0 1 4𝑋4
1 0 2 1 1 1 1 1 2 −1 −1 0
𝑨 = ( 2 −1 3 1) 𝑩 = (1 1 −1 −1 ) 𝑪 = (−1 1 0 −1)
−3 1 0 1 1 −1 1 −1 −1 0 2 −1
2 −1 3 0 4𝑋4 1 −1 −1 1 4𝑋4 0 −1 −1 1 4𝑋4