Write a brief essay (*suggested length of 1–2 pages*) in which you do the following:

Justify that the **ten** statements are logically equivalent to the statement “The *n* × *n* matrix *A *is invertible.”

(a) *A* is an invertible matrix.

(b) *A* is row equivalent to the *n* × *n* identity matrix.

(c) *A* has *n* pivot positions.

(d) The equation *Ax* = 0 has only the trivial solution.

(e) The equation *Ax* = *b* has at least one solution for each *b* in **R**^{n}

(f) The columns of *A* span **R**^{n}

(g) The linear transformation *x *→ *Ax *maps **R*** ^{n}* onto

(h) There is an *n *×* n* matrix *C* such that *CA = I.*

(i) There is an *n *×* n* matrix *D *such that *AD = I.*

(j) The columns of *A* form a basis of **R*** ^{n}*.

This does not have to be a Þ b, aÞ c, aÞ d, etc.However all statements must connect in some way.Example aÞ bÞ cÞ dÞ eÞ fÞ gÞ hÞ iÞ jÞ a.

Subject | Mathematics |

Due By (Pacific Time) | 06/22/2013 09:00 pm |

Tutor | Rating |
---|---|

pallavi Chat Now! |
out of 1971 reviews More.. |

amosmm Chat Now! |
out of 766 reviews More.. |

PhyzKyd Chat Now! |
out of 1164 reviews More.. |

rajdeep77 Chat Now! |
out of 721 reviews More.. |

sctys Chat Now! |
out of 1600 reviews More.. |

sharadgreen Chat Now! |
out of 770 reviews More.. |

topnotcher Chat Now! |
out of 766 reviews More.. |

XXXIAO Chat Now! |
out of 680 reviews More.. |