INNOVATION IN EDUCATION: Matrices and Determinants II

BCA

Practice Questions

Matrices and Determinants

Q1 Find A^-1

^{Q2 IF}

^{a) A+B, Check if A+B=B+A}
^{b) A-B}
c) B-A, Check if A-B=B-A

d) AXB, Check if AXB=BXA

e) (A)'

f ) A²
g) 3A + A²

Q 3 IF
$A=\begin{bmatrix} \frac{3}{2} & 2 &8 &1\\ 2& \frac{-1}{2} &5 &2\\ 1&3 & 11&3 \\ 1&1 & 9 & 1 \end{bmatrix} B=\begin{bmatrix} \frac{3}{5} & 2 &8& 2\\ 2& \frac{-3}{2} &5&1 \\ 1&3 & 9&5 \\ 1&3 & 9 &3 \end{bmatrix}$
a) A-B

b) A X B

Q4 Find the determinant of the following

$a) \begin{vmatrix} 1 &8 \\ 5&3 \end{vmatrix}$

$b) \begin{vmatrix} 1 &8&2 \\ 5&3&1 \\ 4&3&2 \end{vmatrix}$

$c) \begin{vmatrix} 1 &8&2 &1\\ 5&3&1&2 \\ 4&3&2&1\\ 4&3&2&1 \end{vmatrix}$

Solutions

Ans 1

$A^{-1}=\begin{bmatrix} \frac{-39}{2} &6 & 14\\ -13 &\frac{11}{2} &\frac{17}{2} \\ \frac{13}{2}& \frac{-5}{2} & \frac{-19}{2} \end{bmatrix}$

Ans 2

a)
$A+B=\begin{bmatrix} \frac{21}{10} & 4 & 16 \\ 4& -2 & 10\\ 2& 6 & 18 \end{bmatrix}$

$B+A=\begin{bmatrix} \frac{21}{10} & 4 & 16 \\ 4& -2 & 10\\ 2& 6 & 18 \end{bmatrix}$

hence A+B=B+A

b)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 \\ 0& 1 & 0\\ 0& 0 & 0 \end{bmatrix}$

c)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 \\ 0& 1 & 0\\ 0& 0 & 0 \end{bmatrix}$

$B-A=\begin{bmatrix} \frac{-9}{10} & 0 & 0 \\ 0& -1 & 0\\ 0& 0 & 0 \end{bmatrix}$

hence A-B is not equal to B-A

d)
$A X B=\begin{bmatrix} \frac{129}{10} & 24 & 94\\ \frac{26}{5}& \frac{79}{4} &\frac{117}{2} \\ \frac{78}{5}& \frac{49}{2} & 104 \end{bmatrix}$

$B X A= \begin{bmatrix} \frac{129}{10} & \frac{121}{5} & \frac{434}{5}\\ 5 & \frac{79}{4} & \frac{107}{2} \\ \frac{33}{2} & \frac{35}{2}& 104 \end{bmatrix}$

Hence AXB is not equal to BXA
e)
$A'=\begin{bmatrix} \frac{3}{2} &2 &1 \\ 2& \frac{-1}{2} &3 \\ 8& 5 &9 \end{bmatrix}$

f)
$A^2=\begin{bmatrix} \frac{57}{4} &26 &94 \\ 7& \frac{77}{4} &\frac{117}{2} \\ \frac{33}{2}& \frac{55}{2} &104 \end{bmatrix}$

g)

$3A+A^2=\begin{bmatrix} \frac{75}{4}& 32 & 118 \\ 13& \frac{71}{4} & \frac{147}{2}\\ \frac{39}{2}&\frac{73}{2} & 131 \end{bmatrix}$

Ans 3

a)
$A-B=\begin{bmatrix} \frac{9}{10} & 0 & 0 & -1\\ 0& 1 &0 &1 \\ 0 &0 &2 &-2 \\ 0& -2 & 0 & -2 \end{bmatrix}$

b)
$A X B=\begin{bmatrix} \frac{139}{10} & 27 & 103 & 48\\ \frac{36}{5}& \frac{103}{4} &\frac{153}{2} &\frac{69}{2} \\ \frac{103}{5}&\frac{79}{2} &149 &69 \\ \frac{63}{5}&\frac{61}{2} & 103 & 51 \end{bmatrix}$

Ans 4

a) -37

b)
$\frac{-13}{4}$

c) 0

1 comment:

xenikgagelNovember 8, 2022 at 8:47 PM
Less than 1 p.c of individuals with a gambling drawback seek help, in accordance with Whyte. Regardless of the legality, the growing prevalence of gambling in society helped him legitimize his habit to 토토사이트 himself. It felt less “seedy,” he mentioned, even when he would gamble till three in the morning whereas his kids slept “and then get up and do it again.” By this 12 months, Jason didn’t go a day with out gambling. One of vital thing} causes behind the stigma is the stereotypical notion of these dealing with gambling dysfunction as being impulsive, irrational, irresponsible and aggressive. The desire to cover their circumstances could lead to a decrease variety of people with gambling dysfunction to seek help.

Translate

Sunday, July 28, 2019

Matrices and Determinants II

1 comment:

Contact Form