Chapter 11, Matrices Video Solutions, Engineering Mathematics Through Applications

Problem 1

For $\mathbf{A}=\left(\begin{array}{rr}1 & 2 \\ 3 & -1\end{array}\right), \mathbf{B}=\left(\begin{array}{rr}6 & -1 \\ 5 & 3\end{array}\right)$ and $\mathbf{C}=\left(\begin{array}{r}-1 \\ 1\end{array}\right)$, evaluate the following:
$\mathbf{a} \mathbf{A}+\mathbf{B}$
b $\mathbf{B}+\mathbf{A}$
$\mathbf{c} \mathrm{A}+\mathrm{A}+\mathrm{A}$
d $3 \mathrm{~A}+2 \mathrm{~B}$
e $\mathrm{A}+\mathrm{C}$ f $\mathrm{B}+\mathrm{C}$
$\mathbf{g} \mathrm{AC}$
h BC
i $5 \mathrm{~A}-7 \mathrm{BC}$
j $3 \mathrm{AC}-2 \mathrm{BC}$

Vishnu P

Numerade Educator

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Problem 2

Write down the matrix representing the ABCDEFGH in Fig. 10 below:

Victor Salazar

Numerade Educator

01:10

Problem 3

Let the top of a table be given by the co-ordinates $P(1,2), Q(2,2), R(2,4)$ and $S(1,4)$. Write down the matrix A which represents this table top PQRS.
Let
$$
\begin{aligned}
&\mathbf{B}=\left(\begin{array}{llll}
4 & 4 & 4 & 4 \\
0 & 0 & 0 & 0
\end{array}\right), \mathbf{C}=\left(\begin{array}{rr}
0 & 1 \\
-1 & 0
\end{array}\right) \text { and } \\
&\mathbf{D}=\left(\begin{array}{rr}
-1 & 0 \\
0 & 1
\end{array}\right)
\end{aligned}
$$
Determine the image of the table top under the following transformation and illustrate the effect that each transformation has:
e CD(A) f DC(A)

Lucía Guerrero

Numerade Educator

03:17

Problem 4

Let $\mathbf{A}=\left(\begin{array}{ll}1 & -1 \\ 1 & -1\end{array}\right)$ and find $\mathbf{A}^{2}=\mathbf{A} \times \mathbf{A}$. [A $^{2}$ in MATLAB is evaluated by the command $\left.A^{\wedge} 2 .\right]$ Comment upon your result. Can you get the same result when multiplying two non-zero real numbers?

Willis James

Numerade Educator

00:24

Problem 5

Evaluate $\left(\begin{array}{rrr}5 & -1 & -2 \\ 10 & -2 & -4 \\ 15 & -3 & -6\end{array}\right)\left(\begin{array}{rrr}1 & 1 & 3 \\ 1 & -1 & -1 \\ 2 & 3 & 8\end{array}\right)$.
Comment upon your result. Can you get the same result when multiplying two non-zero real numbers?

Joshua Eastwood

Numerade Educator