Simultaneous Linear Equations http:numericalmethods'eng'usf'edu Numerical Methods for the STEM under

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Simultaneous Linear Equationshttp//numericalm
ethods.eng.usf.eduNumerical Methods for the STEM
undergraduate
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The name of the person in the picture is

• Yung Joc
• T-Pain
• 50 cent
• MC Hammer

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The size of matrix
is

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The c32 entity of the matrix

• 2
• 3
• 6.3
• does not exist

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Given
then if CAB, c12

• 0
• 6
• 12

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Given
then if CA-B, c23

• -3
• 3
• 9

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A square matrix A is lower triangular if

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A square matrix A is upper triangular if

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An identity matrix I needs to satisfy the
following

matrix is square
all of the above
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Given
then if CAB, then c31 .

• -57
• -45
• 57
• Does not exist

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The following system of equations x y26x
6y12has solution(s).

• no
• one
• more than one but finite number of
• infinite

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Three kids-Jim, Corey and David receive an
inheritance of 2,253,453. The money is put in
three trusts but is not divided equally to begin
with. Coreys trust is three times that of
Davids because Corey made and A in Dr.Kaws
class. Each trust is put in and interest
generating investment. The total interest of all
the three trusts combined at the end of the first
year is 190,740.57 . The equations to find the
trust money of Jim (J), Corey (C) and David (D)
in matrix form is

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The goal of forward elimination steps in Naïve
Gauss elimination method is to reduce the
coefficient matrix to a (an) _________
matrix.

• diagonal
• identity
• lower triangular
• upper triangular

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Division by zero during forward elimination steps
in Naïve Gaussian elimination of the set of
equations AXC implies the coefficient
matrix A

• is invertible
• is nonsingular
• is singular
• cannot be determined to be singular or
  nonsingular

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Division by zero during forward elimination steps
in Gaussian elimination with partial pivoting of
the set of equations AXC implies the
coefficient matrix A

• is invertible
• is nonsingular
• is singular
• cannot be determined to be singular or
  nonsingular

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LU decomposition method is computationally more
efficient than Naïve Gauss elimination for solving

• a single set of simultaneous linear equations
• multiple sets of simultaneous linear equations
  with different coefficient matrices and same
  right hand side vectors.
• Multiple sets of simultaneous linear equations
  with same coefficient matrix and different right
  hand side vectors
• none of the above

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For a given 1000x1000 matrix A, assume that it
takes about 15 seconds to find the inverse of A
by the use of the LU decomposition. The
approximate time in seconds, that will take to
find the inverse if found by repeated use of
Naïve Gauss Elimination method is

• 150
• 750
• 3750
• 15000

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THE END
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Consider there are only two computer companies in
a country. The companies are named Dude and Imac.
Each year, company Dude keeps 1/5th of its
customers, while the rest switch to Imac. Each
year, Imac keeps 1/3rd of its customers, while
the rest switch to Dude. If in 2003, Dude had
1/6th of the market and Imac had 5/6th of the
marker, what will be share of Dude computers when
the market becomes stable?

• 37/90
• 5/11
• 6/11
• 53/90

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Given
then A is a matrix.

• diagonal
• identity
• lower triangular
• upper triangular

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A square matrix
is diagonally dominant if

• 
  

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The following data is given for the velocity of
the rocket as a function of time. To find the
velocity at t21s, you are asked to use a
quadratic polynomial v(t)at2btc to approximate
the velocity profile.

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An example of upper triangular matrix is

none of the above
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An example of lower triangular matrix is

none of the above