Matrices Worksheets

Matrix Worksheets

1Given the matrices:

Calculate:

(A + B)²;       (A - B)²;       (B)³;        A · B^t · C.

2Prove that: A² − A − 2 I = 0, where:

3 Given the matrix A =  . Find Aⁿ , for n
4Determine the matrix that is needed to premultiply by the matrix
in order to obtain the matrix .
5Find all matrices that commute with the matrix:

6 Determine the matrices A and B that verify the system:

7  A factory produces two models of washing machines, A and B, in three available finishes: N, L and S. Model A is produced in 400 units in Finish N, 200 units in Finish L and 50 units in Finish S. Model B is produced in 300 units in Finish N, 100 units in Finish L and 30 units in Finish S. Finish N takes 25 hours of workshop time to complete and 1 hour of administration. Finish L takes 30 hours of workshop time and 1.2 hours of administration. Finally, Finish S takes 33 hours of workshop time and 1.3 hours of administration.
1.Represent the information in two matrices.
2.Find a matrix that expresses the hours of workshop and administration time needed for each of the models.
8A furniture company manufactures three different models of shelves: A, B and C. Each of these models is offered in both large and small sizes. Everyday, the factory produces 1,000 large and 8,000 small shelves in Type A, 8,000 large and 6,000 small shelves in Type B and 4,000 large and 6,000 small shelves in Type C. Regardless of the type, each large shelf has 16 screws and 6 supporting brackets while each small shelf has 12 screws and 4 supporting brackets.

1Represent this information in two matrices.

2Find a matrix that represents the quantity of screws and supports brackets necessary for daily production of each of the six model-sized shelves.

9Given the matrices:

Calculate the value of X in the following equations:

Prove that: A² − A − 2 I = 0, where:

Given the matrix A = . Find Aⁿ , for n

Top 10 Horror Movies Ever

#10 Best Horror Movie
of All Times

Halloween

Best Horror Movie Directed by John Carpenter

Halloween is as pure and undiluted as its title. In the small town of Haddonfield, Illinois, a teenage baby sitter tries to survive a Halloween night of relentless terror, during which a knife-wielding maniac goes after the town's hormonally charged youths.

Director John Carpenter takes this simple situation and orchestrates a superbly mounted symphony of horrors. It's a movie much scarier for its dark spaces and ominous camera movements than for its explicit bloodletting.

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#9 Best Horror Movie
of All Times

Night of the Living Dead

Horror Movie Directed by George A. Romero

We can hardly imagine how shocking this film was when it first broke into the film scene in 1968. There's never been anything quite like it again, though there have been numerous pale imitations.

Part of the terror lies in the fact that it is shot in such a raw and unadorned fashion that it feels like a home movie, and is all the more authentic because of that. It draws us into its world gradually, content to establish a merely spooky atmosphere before leading us through a horrifically logical progression that we hardly could have anticipated.

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#8 Best Horror Movie
of All Times

Dawn of the Dead

Horror Movie Directed by George A. Romero

George Romero's 1978 follow-up to his classic Night of the Living Dead is quite terrifying and gory (those zombies do like the taste of living flesh). But in its own way, it is just as comically satiric as the first film in its take on contemporary values.

This time, we follow the fortunes of four people who lock themselves inside a shopping mall to get away from the marauding dead and who then immerse themselves in unabashed consumerism, taking what they want from an array of clothing and jewelry shops, making gourmet meals, etc. It is Romero's take on Louis XVI in the modern world: keep the starving masses at bay and crank up the insulated indulgence.

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#7 Best Horror Movie
of All Times

Rosemary's Baby

Horror Movie Directed by Roman Polanski

Psychological terrorism and supernatural horror have rarely been dramatized as effectively as in this classic 1968 thriller, masterfully adapted and directed by Roman Polanski from the chilling novel by Ira Levin.

Rosemary (Mia Farrow) is a young, trusting housewife in New York whose actor husband (John Cassavetes), unbeknownst to her, has literally made a deal with the devil. In the thrall of a witches' coven headquartered in their apartment building, the young husband arranges to have his wife impregnated by Satan in exchange for success in a Broadway play.

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#6 Best Horror Movie
of All Times

Jaws

Horror Movie Directed by Steven Spielberg

The story of a Long Island town whose summer tourist business is suddenly threatened by great-white-shark attacks on humans bypasses the potboiler trappings of Benchley's book and goes straight for the jugular with beautifully crafted, crowd-pleasing sequences of action and suspense supported by a trio of terrific performances by Roy Scheider (as the local sheriff), Richard Dreyfuss (as a shark specialist), and particularly Robert Shaw (as the old fisherman who offers to hunt the shark down). The sequences on Shaw's boat--as the three of them realize that in fact the shark is hunting them--are what entertaining moviemaking is all about.

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Jaws (30th Anniversary Edition)

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#5 Best Horror Movie
of All Times

The Exorcist

Horror Movie Directed by William Friedkin

The frightening and realistic tale of an innocent girl inhabited by a terrifying entity, her mother's frantic resolve to save her and two priests--one doubt-ridden, the other a rock of faith--joined in battling ultimate evil always leaves viewers breathless. This greatest supernatural thriller of all time astonishes and unsettles like no other movie.

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The Exorcist (Extended Director's Cut)

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#4 Best Horror Movie
of All Times

The Thing

Horror Movie Directed by John Carpenter

Researchers in the remote Antarctic discover the remains of a spacecraft that has long been frozen in the ice. However they are confronted by a shape-shifting alien that assumes the appearance of the people that it kills.

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The Thing (1982) Trailer

Best Horror Movie Trailer

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#3 Best Horror Movie
of All Times

The Shining

Horror Movie Starring Jack Nicholson

In this masterpiece adapted from Steven King's novel, a family moves to an isolated mountain resort for the winter where the father falls prey to haunting forces and influence him into violence. On the other hand his son sees horrific visions from the past and the future.

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#2 Best Horror Movie
of All Times

Alien

Horror Movie Directed by Ridley Scott

The terror begins when the crew of a spaceship investigates a transmission from a desolate planet, and discovers a life form that is perfectly evolved to annihilate mankind.

One by one, each crew member is slain until only Ripley is left, leading to an explosive conclusion that sets the stage for its stunning sequel, "Aliens."

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Alien Quadrilogy (Alien/ Aliens /Alien 3 /Alien Resurrection)

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#1 Best Horror Movie
of All Times

Psycho

Horror Movie Directed by Alfred Hitchcock

One of the most shocking films of all time, Alfred Hitchcock's Psycho is now available on Blu-ray featuring perfect picture, a newly created 5.1 audio track and bonus features that take you beyond the movie! Join the Master of Suspense on a chilling journey as an unsuspecting victim (Janet Leigh) visits the Bates Motel and falls prey to one of cinema's most notorious psychopaths - Norman Bates (Anthony Perkins). Named #1 on the AFI's 100 Years Thrills list, this notorious film has become a cultural phenomenon. Featuring one of the most iconic scenes in film history - the famous "shower scene", Psycho is "still terrifying after all these years" (Leonard Maltin's Classic Movie Guide).
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Psycho (Collector's Edition)

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Psycho (50th Anniversary Edition) [Blu-ray]

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