Exam 7: Matrix Algebra

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   and  and    and

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Perform the indicated operation if possible: Perform the indicated operation if possible:      Perform the indicated operation if possible:

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The prices (in dollars per unit)for 3 textbooks are represented by the price vector: P = The prices (in dollars per unit)for 3 textbooks are represented by the price vector: P =    .A university bookstore orders these books in the quantities given by the column vector: Q =    .Use the matrix operations on a graphing calculator to find the total cost (in dollars)of the purchase. .A university bookstore orders these books in the quantities given by the column vector: Q = The prices (in dollars per unit)for 3 textbooks are represented by the price vector: P =    .A university bookstore orders these books in the quantities given by the column vector: Q =    .Use the matrix operations on a graphing calculator to find the total cost (in dollars)of the purchase. .Use the matrix operations on a graphing calculator to find the total cost (in dollars)of the purchase.

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What is the total demand for the four types of energy from both the consumers and the energy industries?

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Reducing Reducing   gives gives

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By looking at the solution of the above question,can you give the number of solutions of the equations? By looking at the solution of the above question,can you give the number of solutions of the equations?

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Use matrix multiplication to represent the system: Use matrix multiplication to represent the system:

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The spa staff determines that a client should take 90% of the RDA of vitamin A,190% of the RDA of vitamin C,and 130% of the RDA of vitamin D each day.Use the matrix operations on a graphing calculator to determine how many tablets of each supplement should she take each day.

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(a)If A is the coefficient matrix of the system (a)If A is the coefficient matrix of the system    ,determine    . (b)Use    to solve the system. ,determine (a)If A is the coefficient matrix of the system    ,determine    . (b)Use    to solve the system. . (b)Use (a)If A is the coefficient matrix of the system    ,determine    . (b)Use    to solve the system. to solve the system.

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If A = If A =   where A is 2 × 2 and   = i - 2j,then matrix A is given by where A is 2 × 2 and If A =   where A is 2 × 2 and   = i - 2j,then matrix A is given by = i - 2j,then matrix A is given by

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Find the inverse matrix of Find the inverse matrix of    . .

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If A = If A =    and B =    ,find A - B. and B = If A =    and B =    ,find A - B. ,find A - B.

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Write a diagonal matrix of size 3 × 3 with entries Write a diagonal matrix of size 3 × 3 with entries    = i + 3,    = 0 for i ≠ j. = i + 3, Write a diagonal matrix of size 3 × 3 with entries    = i + 3,    = 0 for i ≠ j. = 0 for i ≠ j.

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Find x,y,z,u,t,v such that Find x,y,z,u,t,v such that    + 2    =  + 2 Find x,y,z,u,t,v such that    + 2    =  = Find x,y,z,u,t,v such that    + 2    =

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If If   ,then ,then

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If A = If A =    ; B =    ,then find (A +    . ; B = If A =    ; B =    ,then find (A +    . ,then find (A + If A =    ; B =    ,then find (A +    . .

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Let A = Let A =    ; B =    ; C =    .Find A  ; B = Let A =    ; B =    ; C =    .Find A  ; C = Let A =    ; B =    ; C =    .Find A  .Find A Let A =    ; B =    ; C =    .Find A

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An electronics store has 35 televisions,15 VCRs,and 25 CD players in stock.If the value of each television is $400,each VCR is $200 and each CD player is $150,use the matrix operations on a graphing calculator to find the total value of the electronics store's inventory.

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If A is a 3 × 5 matrix,B is a 5 × 7 matrix,C is a 7 × 11 matrix,D is a 5 × 7 matrix,which of the following matrix products are defined? Give the size of each answer if it is defined. (a)A × B × C (b)B × C × D (c)A × D × C (d)A × B × D

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For what values of a will the following system of equations have a solution? For what values of a will the following system of equations have a solution?

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