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Mathematics

2 answers:

alexira [117]3 years ago

6 0

Answer:

$- \frac{3}{7}$

Step-by-step explanation:

th first thing your gonna do is to multiply the number out side of each parentheses with the inside number. so 3 (3x-1)=9x-3 and 2 (3-x)= 6-2x. Now your equation 9x-3+6-2x=0. Then group all of the like terms. -3+6+9x-2x=0, -3+6=3 and 9x-2x=7x. 3+7x=0. Minus 7x on both sides to get rid of zero 3=-7x then divide by -7 to find x. 3 divide by -7 =

$- \frac{3}{7 }$

ahrayia [7]3 years ago

3 0

Answer: x= 3/7

Step-by-step explanation:

Simplifies to:

9x-9+6-2x=0

7x-3=0

7x=3

X=3/7

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Find the characteristic polynomial of A. Use x for the variable in your polynomial.You do not need to factor your polynomial. A

Vesna [10]

Answer: The required characteristic polynomial of the given matrix A is $x^3+6x+11x+6=0.$

Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :

$A=\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right].$

We know that

for any square matrix M, the characteristic polynomial is given by

$|M-xI|=0,$ where I is an identity matrix of same order as M.

Therefore, the characteristic polynomial of matrix A is

$|A-xI|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}0&0&1\\4&-3&4\\-2&0&-3\end{array}\right]-x\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\right|=0\\\\\\\Rightarrow \left|\left[\begin{array}{ccc}-x&0&1\\4&-3-x&4\\-2&0&-3-x\end{array}\right] \right|=0\\\\\\\Rightarrow -x(3+x)^2+1(0-6-2x)=0\\\\\Rightarrow (x+3)(-3x-x^2-2)=0\\\\\Rightarrow (x+3)(x^2+3x+2)=0\\\\\Rightarrow x^3+6x+11x+6=0.$