Matrices: Understanding Systems of Equations with Examples

Multiply the following matrices:
$A = [\begin{matrix} - 2 & 1 & 5 \\ 1 & 4 & - 5 \end{matrix}] B = [\begin{matrix} - 1 & 7 \\ 2 & - 2 \\ 3 & 4 \end{matrix}]$ AB=?

Reggie 2020-12-15

Define is subtraction of matrices commutative and associative?

Falak Kinney 2020-12-15

Determine the null space of each of the following matrices:
$(\begin{matrix} 1 & 2 & - 3 & - 1 \\ - 2 & - 4 & 6 & 3 \end{matrix})$

kuCAu 2020-12-12

verify that $(A B)^{T} = B^{T} A^{T}$
If $A = [\begin{matrix} 2 & 1 \\ 6 & 3 \\ - 2 & 4 \end{matrix}] and B = [\begin{matrix} 2 & 4 \\ 1 & 6 \end{matrix}]$

Lennie Carroll 2020-12-09

Given the matrices A and B shown below , solve for X in the equation $- \frac{1}{3} X + \frac{1}{2} A = B$
$A = [\begin{matrix} - 10 & 4 \\ 8 & 8 \end{matrix}], B = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]$

Joni Kenny 2020-12-09

Identify orthogonal matrices Invert orthogonal matrice
$[\begin{matrix} \frac{1}{3} & \frac{2}{3} & \frac{2}{3} \\ \frac{2}{3} & \frac{1}{3} & - \frac{2}{3} \\ \frac{2}{3} & - \frac{2}{3} & \frac{1}{3} \end{matrix}]$

Khaleesi Herbert 2020-12-07

Tell whether it’s matrices is in. Reduced form and the solution. If it’s not then give the row operation required to put it into reduced form
$[\begin{matrix} 1 & 0 & - 4 & | & 0 \\ 0 & 1 & 2 & | & 0 \\ 0 & 0 & 0 & | & 1 \end{matrix}]$

waigaK 2020-12-07

Use the given coding matrices to encode and then decode the given message HELP.
$A = [\begin{matrix} 4 & - 1 \\ - 3 & 1 \end{matrix}]$ and its inverse $A^{- 1} = [\begin{matrix} 1 & 1 \\ 3 & 4 \end{matrix}]$

Cabiolab 2020-12-07

Find the determinants in Exercise , assuming that
$| \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} | = 4$
$| \begin{matrix} 2 a & 2 b & 2 c \\ d & e & f \\ g & h & i \end{matrix} |$

Khadija Wells 2020-12-07

Let $A = [\begin{matrix} 1 & 2 \\ - 1 & 1 \end{matrix}] and C = [\begin{matrix} - 1 & 1 \\ 2 & 1 \end{matrix}]$
a)Find elementary matrices $E_{1} and E_{2}$ such that $C = E_{2} E_{1} A$
b)Show that is no elementary matrix E such that $C = E A$

Yulia 2020-12-06

Show that A and B are not similar matrices
$A = [\begin{matrix} 1 & 0 & 1 \\ 2 & 0 & 2 \\ 3 & 0 & 3 \end{matrix}], B = [\begin{matrix} 1 & 1 & 0 \\ 2 & 2 & 0 \\ 0 & 1 & 1 \end{matrix}]$

pedzenekO 2020-12-05

$A = [\begin{matrix} 1 & - 3 & 3 \\ 1 & 0 & - 2 \end{matrix}], B = [\begin{matrix} - 3 & 1 & 2 \\ 2 & 5 & - 3 \end{matrix}]$
Find 2B?

nitraiddQ 2020-12-05

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1),(1, 1),(1, 2),(2, 0),(2, 2),(3, 0). Find reflexive, symmetric and transitive closure of R.

postillan4 2020-12-05

Find the inverse of each of the following matrices.
$[\begin{matrix} 1 & 0 & 1 \\ - 1 & 1 & 1 \\ - 1 & - 2 & - 3 \end{matrix}]$

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.

Isa Trevino 2020-12-03

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

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?

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 $t r (A) = t r (A^{t})$

Even if you have never worked with matrices equations before, it is high time to dive into this interesting topic as you look up various questions and receive professional help by turning to our matrices examples. Remember that these are used in encryption, economics, video games, animation, and all kinds of physics where quantum mechanics and optics are involved. Since there are matrices problems based on equations, we also provide you with the answers that will help you find the most efficient solutions and challenge yourself with more than one mathematical analysis method.

Precalculus

Learn Matrices: Practice Problems and Examples