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Foster James

Foster J.

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Let $A$ and $B$ be $n \times n$ matrices and let $C=A B .$ Prove that if $B$ is singular then $C$ must be singular. Hint: Use Theorem $1.5 .2 .$

Linear Algebra with Application

Matrices and Systems of Equations

Elementary Matrices

Let $A$ be a $3 \times 3$ matrix and suppose that $$ a_{1}=3 a_{2}-2 a_{3} $$ Will the system $A x=0$ have a nontrivial solution? Is $A$ nonsingular? Explain your answers.

Linear Algebra with Application

Matrices and Systems of Equations

Elementary Matrices

Use back substitution to solve each of the following systems of equations: $ \begin{aligned} \text { (a) } x_{1}-3 x_{2} &=2 \\ 2 x_{2} &=6 \end{aligned}$ $\begin{aligned} \text { (b) } x_{1}+x_{2}+x_{3} &=8 \\ 2 x_{2}+x_{3} &=5 \\ 3 x_{3} &=9 \end{aligned}$ $\begin{aligned} \text { (c) } x_{1}+2 x_{2}+2 x_{3}+x_{4} &=5 \\ 3 x_{2}+x_{3}-2 x_{4} &=1 \\-x_{3}+2 x_{4} &=-1 \\ 4 x_{4} &=4 \end{aligned}$ $$ \begin{array}{ll}{\text { (d) } x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=5} \\ {2 x_{2}+x_{3}-2 x_{4}+x_{5}=1} \\ {4 x_{3}+x_{4}-2 x_{5}=1} \\ {x_{4}-3 x_{5}=0} \\ {\qquad 2 x_{5}=2}\end{array} $$

Use back substitution to solve each of the following systems of equations: $ \begin{aligned} \text { (a) } x_{1}-3 x_{2} &=2 \\ 2 x_{2} &=6 \end{aligned}$ $\begin{aligned} \text { (b) } x_{1}+x_{2}+x_{3} &=8 \\ 2 x_{2}+x_{3} &=5 \\ 3 x_{3} &=9 \end{aligned}$ $\begin{aligned} \text { (c) } x_{1}+2 x_{2}+2 x_{3}+x_{4} &=5 \\ 3 x_{2}+x_{3}-2 x_{4} &=1 \\-x_{3}+2 x_{4} &=-1 \\ 4 x_{4} &=4 \end{aligned}$ $$ \begin{array}{ll}{\text { (d) } x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=5} \\ {2 x_{2}+x_{3}-2 x_{4}+x_{5}=1} \\ {4 x_{3}+x_{4}-2 x_{5}=1} \\ {x_{4}-3 x_{5}=0} \\ {\qquad 2 x_{5}=2}\end{array} $$

Linear Algebra with Application

Matrices and Systems of Equations

Systems of Linear Equations

A very long, straight wire has charge per unit length $1.47 \times 10^{-10} \mathrm{C} / \mathrm{m}$. At what distance from the wire is the electric-field magnitude equal to $2.52 \mathrm{~N} / \mathrm{C} ?$

A very long, straight wire has charge per unit length $1.47 \times 10^{-10} \mathrm{C} / \mathrm{m}$. At what distance from the wire is the electric-field magnitude equal to $2.52 \mathrm{~N} / \mathrm{C} ?$

University Physics with Modern Physics In SI Units

Questions asked

ANSWERED

David Nguyen verified

Numerade educator

A factory uses 3 machines M1;M2;M3 to produce certain items. M1 produces 50% of the items, of which 3% are defective. M2 produces 30% of the items, of which 4% are defective. M3 produces 20% of the items, of which 5% are defective. Suppose that a defective item is found. What is the probability that it came from M2?

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ANSWERED

David Nguyen verified

Numerade educator

In some states, license plates have six characters: three letters followed by three numbers. How many distinct such plates are possible?

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ANSWERED

David Nguyen verified

Numerade educator

An 8-bit binary word is a sequence of 8 digits, of which each may be either a 0 or a 1. How many di erent 8-bit words are there?

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ANSWERED

David Nguyen verified

Numerade educator

A class has 12 boys and 18 girls. In how many ways can the teacher choose 1 boy and 1 girl as representatives to the student government?

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ANSWERED

Vincenzo Zaccaro verified

Numerade educator

Find the probability of the following events. a. A randomly chosen integer x 2 [0; 999] is divisible by 11. b. A randomly chosen integer x 2 [0; 999] is divisible by 13. c. A randomly chosen integer x 2 [0; 999] is divisible by 11 or 13.

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ANSWERED

David Nguyen verified

Numerade educator

A hand of 5 cards is drawn randomly from a standard deck of 52 cards. Let X be the number of hearts contained in the hand of 5 cards. (a) Find the set of possible values of X. (b) Write down the PMF and the CDF of X, that is, nd p(x) and F(x) for all the values x in part (a).

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ANSWERED

Kirsty Gledhill verified

Numerade educator

(a) Find c so that f(x) is the PDF of a continuous random variable X.

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ANSWERED

Robin Corrigan verified

Numerade educator

X = time (in years) until the next eruption of a volcano. Assume X  Exp(0:001). What is the probability for an eruption within the next 100 years?

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ANSWERED

T. L. verified

Numerade educator

The IQ scores of a large population follow a normal distribution with  = 100 and  = 15. An individual is selected at random. What is the probability that his score X satis es 100 < X < 115?

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