Resol l'equació A X B = C t AXB=C^{\ t\ } A X B = C t

X = A − 1 ⋅ C t ⋅ B − 1 X=A^{-1}\cdot C^{t\ }\cdot B^{-1} X = A − 1 ⋅ C t ⋅ B − 1

X = B − 1 ⋅ C t ⋅ A − 1 X=B^{-1}\cdot C^{t\ }\cdot A^{-1} X = B − 1 ⋅ C t ⋅ A − 1

X = A − 1 ⋅ B − 1 ⋅ C t X=A^{-1}\cdot B^{-1}\cdot C^{\ t} X = A − 1 ⋅ B − 1 ⋅ C t

X = C t ⋅ A − 1 ⋅ B − 1 X=C^{\ t}\cdot A^{-1}\cdot B^{-1} X = C t ⋅ A − 1 ⋅ B − 1

Resol l'equació X A − C = X B XA-C=XB X A − C = X B

X = C ⋅ ( A − B ) − 1 X=C\cdot\left(A-B\right)^{-1} X = C ⋅ ( A − B ) − 1

X = C ⋅ ( B − A ) − 1 X=C\cdot\left(B-A\right)^{-1} X = C ⋅ ( B − A ) − 1

X = ( A − B ) − 1 ⋅ C X=\left(A-B\right)^{-1}\cdot C X = ( A − B ) − 1 ⋅ C

X = C ⋅ A − B − 1 X=C\cdot A-B^{-1} X = C ⋅ A − B − 1

Indica lels valors de m m per tal que A A A sigui invertible

para todos los valores de m , m ≠ 1 , m ≠ 3 m,m\ne1,m\ne3 m , m  = 1 , m  = 3

para todos los valores de m ≠ − 1 , m ≠ − 3 m\ne-1,m\ne-3 m  = − 1 , m  = − 3

para m = 1 , m = 3 m=1,m=3 m = 1 , m = 3

para todos los valores de m ≠ 1 m\ne1 m  = 1

El rang màxim d'una matriu 4x5 és?

No es pot calcular el rang perquè no és una matriu quadrada

5 si el determinant 5x5 és diferent de 0

4 si el determinant 5x5 és diferent de zero

Si A i B matrius quadrades d'ordre 2 qualsevol, llavors:

rang(A+B) ≤ \le ≤ rang (A-B)

rang(A) = rang(B) si i només si A=B

Cap de les respostes és correcte

Si el rango de una matriz es 3, entonces

Tiene tantas filas como columnas

Marca la opción correcta

r g ( A ) ≤ 2 rg\left(A\right)\le2 r g ( A ) ≤ 2

r g ( A ) = 3 rg\left(A\right)=3 r g ( A ) = 3

r g ( A ) = 2 rg\left(A\right)=2 r g ( A ) = 2

r g ( A ) ≥ 2 rg\left(A\right)\ge2 r g ( A ) ≥ 2

r g ( A ) ≤ 3 rg\left(A\right)\le3 r g ( A ) ≤ 3

Matrius

Authored by Alex Romero

Mathematics

1st - 8th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

La matriu de la imatge és de dimensió:

2 x 4

2 x 2

4 x 4

4 x 2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

En la matriu IDENTITAT de dimensió 10 x 10, l'el·lement en la posició 9,9 és:

no hi ha el·lement.

MULTIPLE CHOICE QUESTION

30 sec • 5 pts

La matriu de la imatge és:

positiva

triangular

diagonal.

no triangular.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Per multiplicar A_n,m x B_p,r cal que ...

m = p

n = r

m = r

p = n

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Quina afirmació és FALSA?

La matriu I és l'element neutre de la multiplicació.

El producte de matrius és commutatiu.

El producte de matrius és associatiu.

A · O = O on O és la matriu nul·la.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Dadas las siguientes matrices. Calcule a+b

Ninguna

Per sumar dues matrius ......

Han de tenir el mateix ordre

No importa l'ordre de les matrius

Han de tenir diferent ordre

No importa l'ordre sinò els elements de la matriu

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