INNOVATION IN EDUCATION: Matrices and Determinants

Matrices and Determinants

Q1 If

$A=\begin{bmatrix} 1 &3 & 5\\ -6& 1 & 8\\ -1& 3 & 4 \end{bmatrix} B=\begin{bmatrix} 4 &-1 &3 \\ 2 & 5 &4 \\ -9& 2 & 6 \end{bmatrix}$

Find

a) A+B

b) A-B

c) AxB

d) Adj(A)

e) A^-1

^f) (A')

^{Q2 Find the product of the following matrices}

$a)\begin{bmatrix} 3 \\ -1 \\ 9 \end{bmatrix} \begin{bmatrix} 1 & 8 & 6 \end{bmatrix}$

$b)\begin{bmatrix} 1 & 8 & 6 \end{bmatrix} \begin{bmatrix} 3 \\ -1 \\ 9 \end{bmatrix}$

$c) \begin{bmatrix} 1 & 3 &2 \\ -1& 7 &-1 \\ 2& 3& 6 \end{bmatrix} \begin{bmatrix} 2 & 5& 6\\ 1& 3& -2 \end{bmatrix}$

$d) \begin{bmatrix} 1 & 6 &2 \\ 2 & -4 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 &6 \\ 4& 3 & 1\\ 8&6 & 9 \end{bmatrix}$

$e) \begin{bmatrix} 1 & 6 &2 \\ \end{bmatrix} \begin{bmatrix} 1 & 2 &6 \\ 4& 3 & 1\\ 1&6 & 9 \end{bmatrix}$

Q3 Solve the following equation using cramer's rule

2x +   y + z = 3
  x –   y – z = 0
  x + 2y + z = 0

Q4 Find the determinant of the following

$a) \begin{vmatrix} -1 & 4\\ 2& 3 \end{vmatrix}$

$b) \begin{vmatrix} 1 & 3 & -2\\ 6 & 1 & 2\\ 4 & 3 & 7 \end{vmatrix}$

Solutions

Ans 1

$a) \begin{bmatrix} 5 & 2 & 8\\ -4 & 6 & 12\\ -10 & 5 & 10 \end{bmatrix}$

$b) \begin{bmatrix} -3 & 4 & 2\\ -8 & -4 & 4\\ 8 & 1 & -2 \end{bmatrix}$

$c) \begin{bmatrix} -35 & 24 & 45\\ -94 & 27 & 34\\ -34 & 24 & 33 \end{bmatrix}$

$d) \begin{bmatrix} -20 & 3 & 19\\ 16 & 9 & -38\\ -17 & -6 & 19 \end{bmatrix}$

$e) \frac{1}{57}\begin{bmatrix} -20 & 3 & 19\\ 16 & 9 & -38\\ -17 & -6 & 19 \end{bmatrix}$

$f) \begin{bmatrix} 1 & -6 & -1\\ 3 & 1 & 3\\ 5 & 8 & 4 \end{bmatrix}$

Ans 2

$a) \begin{bmatrix} 3 & 24 & 18\\ -3 & -8 & -6\\ 9 & 72 & 54 \end{bmatrix}$

b) [49]

c) Not defined

$d) \begin{bmatrix} 41 & 32 & 30\\ -6 & -2 & 17\\ \end{bmatrix}$

$e) \begin{bmatrix} 27 & 32 & 30\\ \end{bmatrix}$

Ans 3

x=1, y=-2, z=3

Ans 4

a) -11 b) -129

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Thursday, July 25, 2019

Matrices and Determinants

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