Matrices: Understanding Systems of Equations with Examples

Write the given matrix equation as a system of linear equations without matrices.
$[\begin{matrix} 4 & - 7 \\ 2 & - 3 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} - 3 \\ 1 \end{matrix}]$

ediculeN 2021-02-04

Determine whether the given matrices are inverses of each other. $A = [\begin{matrix} 8 & 3 & - 4 \\ - 6 & - 2 & 3 \\ - 3 & 1 & 1 \end{matrix}] and B = [\begin{matrix} - 1 & - 1 & - 1 \\ 3 & 4 & 0 \\ 0 & 1 & - 2 \end{matrix}]$

floymdiT 2021-02-03

Show that the product of two $2 \times 2$ skew symmetric matrices is diagonal. Is this true for $n \times n$ skew symmetric matrices with n > 2?

nicekikah 2021-02-03

Which of the following statements are always true, with A and B are orthogonal matrices?
$1) det (A^{T} (A + B) B^{T}) = det (A^{T} + B^{T})$
$2) det (A^{- 1} + B^{T}) = det (A^{T} + B^{- 1})$
$3) det (A + B^{T}) = det (A^{T} + B)$

Chesley 2021-02-03

$A = [\begin{matrix} 5 & 1 \\ 1 & 1 \end{matrix}]$
$B = [\begin{matrix} 3 & 5 \\ 1 & 3 \end{matrix}]$
Similar or not similar?

Kye 2021-02-03

Detenninants of Sums Give an example of square matrices A and B for which $| A + B | \neq | A | + | B |$

Kye 2021-02-02

Given the matrices
$A = [\begin{matrix} - 1 & 3 \\ 2 & - 1 \\ 3 & 1 \end{matrix}] and B = [\begin{matrix} 0 & - 2 \\ 1 & 3 \\ 4 & - 3 \end{matrix}]$ find the $3 \times 2$ matrix X that is a solution of the equation. 8X+A=B

Line 2021-02-02

Find the following matrices: a) $A + B .$
(b) $A - B .$
(c) -4A.
(d) $3 A + 2 B .$
$A = [\begin{matrix} 6 & 2 & - 3 \end{matrix}], B = [\begin{matrix} 4 & - 2 & 3 \end{matrix}]$

Cheyanne Leigh 2021-02-02

For the following Leslie matrix , find an approximate expression for the population distribution after n years , given that the initial population distribution is given by $X (0) = [\begin{matrix} 2000 \\ 4000 \end{matrix}], L^{n} = [\begin{matrix} 0.8 & 0.4 \\ 1.2 & 0 \end{matrix}]$
Select the correct choice below and fill in the answer boxes to complete your choise.
a) $X \approx () ()^{n} [\begin{matrix} 1 \\ () \end{matrix}]$
b) $X \approx ()^{n} [\begin{matrix} 1 \\ () \end{matrix}]$

shadsiei 2021-02-02

Solve the system of equations (Use matrices.):
$x - 2 y + z = 16$ ,
$2 x - y - z = 14$ ,
$3 x + 5 y - 4 z = - 10$

abondantQ 2021-02-02

compute the indicated matrices (if possible). $D + B C$
Let $A = [\begin{matrix} 3 & 0 \\ - 1 & 5 \end{matrix}], B = [\begin{matrix} 4 & - 2 & 1 \\ 0 & 2 & 3 \end{matrix}], C = [\begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix}], D = [\begin{matrix} 0 & - 3 \\ - 2 & 1 \end{matrix}], E = [\begin{matrix} 4 & 2 \end{matrix}], F = [\begin{matrix} - 1 \\ 2 \end{matrix}]$

Ava-May Nelson 2021-02-02

If $A = (\begin{matrix} 8 & 0 \\ 4 & - 2 \\ 3 & 6 \end{matrix}) and B = (\begin{matrix} 2 & - 2 \\ 4 & 2 \\ - 5 & 1 \end{matrix})$ ,then find the matrix X such that $2 A + 3 X = 5 B$

Ramsey 2021-01-31

Show the concept of addition of matrices Along with an example.

Cheyanne Leigh 2021-01-31

Define Scalar multiplication of matrices?

Khadija Wells 2021-01-31

State the Properties of matrix addition.

Line 2021-01-31

Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
$A = [\begin{matrix} 4 & 1 \\ 3 & 2 \end{matrix}], B = [\begin{matrix} 5 & 9 \\ 0 & 7 \end{matrix}]$

Trent Carpenter 2021-01-31

Let A,B and C be square matrices such that AB=AC , If $A \neq 0$ , then B=C.
Is this True or False?Explain the reasosing behind the answer.

Chardonnay Felix 2021-01-31

Find a basis for the space of $2 \times 2$ diagonal matrices.
$Basis = {[\begin{matrix} \end{matrix}], [\begin{matrix} \end{matrix}]}$

lwfrgin 2021-01-31

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
$A = [\begin{matrix} - 4 & 0 \\ 1 & 3 \end{matrix}], B = [\begin{matrix} - 2 & 4 \\ 0 & 1 \end{matrix}]$

naivlingr 2021-01-31

Solve the system of given equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
${\begin{cases} 3 a - b - 4 c = 3 \\ 2 a - b + 2 c = - 8 \\ a + 2 b - 3 c = 9 \end{cases}$

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