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Find the characteristic polynomial of the matrices
$[\begin{matrix} 2 & 1 \\ - 1 & 3 \end{matrix}]$

Bevan Mcdonald 2020-12-03

Rational functions can have any polynomial in the numerator and denominator. Analyse the key features of each function and sketch its graph. Describe the common features of the graphs.

$a) f (x) = \frac{x}{x^{2} - 1}$

$b) g (x) = \frac{x - 2}{x^{2} + 3 x + 2}$

$c) h (x) = \frac{x + 5}{x^{2} - x - 12}$

allhvasstH 2020-12-03

Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges.
$1 - 2 + 4 - 8 + . . . + (- 1)^{n - 1} 2^{n - 1} + . . .$

Wotzdorfg 2020-12-03

The augmented matrix of a set of linear equations in the variables x, y, and z is shown below. It's presented in condensed row-echelon form.
$[\begin{matrix} 1 & 0 & - 1 & 3 \\ 0 & 1 & 2 & 5 \\ 0 & 0 & 0 & 0 \end{matrix}]$
Find: (a) The leading variables, (b) Is the system in consistent or dependent? (c) The solution of the system.

Jerold 2020-12-03

Determine:
$[\begin{matrix} 1 & - 1 & 2 \end{matrix}] {[\begin{matrix} 4 \\ - 1 \\ 0 \end{matrix}] [\begin{matrix} 2 & 3 \end{matrix}] + [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & - 1 \end{matrix}]}$

beljuA 2020-12-03

If A and B are both $n \times n$ matrices (of the same size), then
det(A+B)=det(A)+det(B)
True or False?

Chesley 2020-12-02

find the product of AB?
$A = [\begin{matrix} 3 & 1 \\ 6 & 0 \\ 5 & 0 \end{matrix}]$
$B = [\begin{matrix} 1 & 5 & 3 \\ - 1 & 2 & - 3 \end{matrix}]$
a) $[\begin{matrix} 2 & 17 & 6 \\ 6 & 30 & 18 \\ 5 & 25 & 15 \end{matrix}]$
b) $[\begin{matrix} 16 & 6 & 18 \\ - 2 & 10 & - 30 \\ 25 & 17 & 6 \end{matrix}]$
c) $[\begin{matrix} 21 & 6 & - 23 \\ 2 & 30 & 5 \\ - 25 & 12 & 17 \end{matrix}]$
d) The product is not defined

pedzenekO 2020-12-02

Graph each polynomial function. $f (x) = x^{3} + 2 x^{2} - 5 x - 6$

Yulia 2020-12-02

Explain why each of the following algebraic rules will not work in general when the real numbers a and b are replaced by $n \times n$ matrices A and B. $a) (a + b)^{2} = a^{2} + 2 a b + b^{2}$
$b) (a + b) (a - b) = a^{2} - b^{2}$

Haven 2020-12-02

Let A and B be $n \times n$ matrices. Recall that the trace of A , written tr(A),equal
$\sum_{i = 1}^{n} A_{i i}$
Prove that tr(AB)=tr(BA) and $t r (A) = t r (A^{t})$

a2linetagadaW 2020-12-01

Let A = {1, 2, 3, 4, 6}, and let R be the relation on A defined by “x divides y”, written as x|y. A. Write R as a set of ordered pairs.

ka1leE 2020-12-01

Find all 2 by 2 matrices that are orthogonal and also symmetric. Which two numbers can be eigenvalues of those two matrices?

Albarellak 2020-12-01

For each of the following matrices, determine a basis for each of the subspaces R(AT ), N(A), R(A), and N(AT ):
$A = [\begin{matrix} 1 & 3 & 1 \\ 2 & 4 & 0 \end{matrix}]$

amanf 2020-11-30

To illustrate the multiplication of matrices, and also the fact that matrix multiplication is not necessarily commutative, consider the matrices
$A = [\begin{matrix} 1 & - 2 & 1 \\ 0 & 2 & - 1 \\ 2 & 1 & 1 \end{matrix}]$
$B = [\begin{matrix} 2 & 1 & - 1 \\ 1 & - 1 & 0 \\ 2 & - 1 & 1 \end{matrix}]$

Jaya Legge 2020-11-30

Let M be the vector space of $2 \times 2$ real-valued matrices.
$M = [\begin{matrix} a & b \\ c & d \end{matrix}]$
and define $M^{#} = [\begin{matrix} d & b \\ c & a \end{matrix}]$ Characterize the matrices M such that $M^{#} = M^{- 1}$

babeeb0oL 2020-11-30

Find the determinate
$A = [\begin{matrix} 4 & 1 \\ 3 & 2 \end{matrix}]$
$B = [\begin{matrix} 2 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 2 & 1 \end{matrix}]$
$C = [\begin{matrix} 3 & - 2 & 0 \\ - 2 & 3 & 0 \\ 0 & 0 & 0 \end{matrix}]$

Kaycee Roche 2020-11-30

Explain why S is not a basis for $M_{2, 2}$
$S = {[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 1 \\ 0 & 0 \end{matrix}]}$

UkusakazaL 2020-11-30

Write the standard form of the complex number.
$12 (\cos (60^{\circ}) + i \sin (60^{\circ}))$

remolatg 2020-11-29

How can the composite function be evaluated?

Anish Buchanan 2020-11-27

Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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