Free Printable Examen de transformaciones lineales

1.

Una propiedad de linealidad de la transformación es:

a)

$T\left(\alpha u\right)<\alpha T\left(u\right)$

b)

$T\left(u+v\right)=T\left(u\right)-T\left(v\right)$

c)

$T\left(\alpha u\right)>\alpha T\left(u\right)$

d)

$T\left(u+v\right)=T\left(u\right)-T\left(v\right)$

2.

a)

$\left(1,1,3\right)$

b)

$\left(-1,1,3\right)$

c)

$\left(-1,1,-1\right)$

d)

$\left(-1,1,-3\right)$

3.

a)

$N\left(t\right)=\left\{\left(-b,b,-b\right);\ b\epsilon R\right\}$

b)

$N\left(t\right)=\left\{\left(a,b,c\right);a,b,c\ \epsilon\ R\right\}$

c)

$N\left(t\right)=\left\{\left(-b,-b,b\right);b\epsilon R\right\}$

d)

$N\left(t\right)=\left\{\left(b,-b,-b\right);\ \ b\epsilon R\right\}$

4.

a)

Uno

b)

Dos

c)

Tres

d)

Cuatro

5.

a)

b)

c)

d)

6.

a)

Uno

b)

Dos

c)

Tres

d)

Cuatro

7.

a)

$T\left(v\right)=\left\{\left(-x,-y,2y\right);x,y\epsilon R\right\}$

b)

$T\left(v\right)=\left\{\left(x,-y,-z\right);x,y\epsilon R\right\}$

c)

$T\left(v\right)=\left\{\left(x,y,-2y\right);x,y\epsilon R\right\}$

d)

$T\left(v\right)=\left\{\left(-x,y,-2y\right);x,y\epsilon R\right\}$

8.

a)

$\lambda=1$

b)

$\lambda=2$

c)

$\lambda=-2$

d)

$\lambda=3$

9.

a)

$E_{\lambda}=\left\{\left(k,0,k\right);\ k\epsilon R\right\}$

b)

$E_{\lambda}=\left\{\left(k,0,-k\right);\ k\epsilon R\right\}$

c)

$E_{\lambda}=\left\{\left(k,0,2k\right);\ k\epsilon R\right\}$

d)

$E_{\lambda}=\left\{\left(2k,0,k\right);\ k\epsilon R\right\}$

10.

a)

b)

c)

d)

Examen de transformaciones lineales

Total questions: 10

Worksheet time: 2hrs 10mins

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