Matrices: Understanding Systems of Equations with Examples

Solve the absolute value equation.
$- 7 (y + 5) < - 9 y - 35$

rocedwrp 2020-12-30

Solve the shown using matrices:
${\begin{cases} 2 x - y - 2 z = - 1 \\ x - 2 y - z = 1 \\ x + y + z = 1 \end{cases}$

Cem Hayes 2020-12-30

Where possible, find the product:
$[\begin{matrix} 2 & 3 & - 1 & 6 \\ 0 & 5 & 4 & 1 \end{matrix}] [\begin{matrix} 1 & 3 \\ 0 & 2 \end{matrix}]$

Lewis Harvey 2020-12-30

Find values for the variables so that the matrices are equal.
$[\begin{matrix} x \\ 7 \end{matrix}] = [\begin{matrix} 11 \\ y \end{matrix}]$

permaneceerc 2020-12-29

If A and B are $n \times n$ diagonalizable matrices , then A+B is also diagonalizable.
True or False?

Haven 2020-12-28

Use the definition of the matrix exponential to compute eA for each of the following matrices:
$A = [\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Kyran Hudson 2020-12-28

Define Invertible Matrices. Give an example.

Cem Hayes 2020-12-28

Explain the concept of Inverse Matrices?

opatovaL 2020-12-27

Perform the indicated matrix operations B - A given that A, B, and C are defined as follows. If an operation is not defined, state the reason.
$A = [\begin{matrix} 4 & 0 \\ - 3 & 5 \\ 0 & 1 \end{matrix}] B = [\begin{matrix} 5 & 1 \\ - 2 & - 2 \end{matrix}] C = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]$

aortiH 2020-12-25

The $2 \times 2$ matrices A and B below are related to matrix C by the equation: $C = 3 A - 2 B$ . Which of the following is matrix C.
$A = [\begin{matrix} 3 & 5 \\ - 2 & 1 \end{matrix}] B = [\begin{matrix} - 4 & 5 \\ 2 & 1 \end{matrix}]$
$[\begin{matrix} - 1 & 5 \\ 2 & 1 \end{matrix}]$
$[\begin{matrix} - 18 & 5 \\ 10 & 1 \end{matrix}]$
$[\begin{matrix} 18 & - 5 \\ - 10 & - 1 \end{matrix}]$
$[\begin{matrix} 1 & - 5 \\ - 2 & - 1 \end{matrix}]$

he298c 2020-12-25

For the given systems of linear equations, determine the values of $b_{1}, b_{2}, and b_{3}$ necessary for the system to be consistent. (Using matrices)
$x - y + 3 z = b_{1}$
$3 x - 3 y + 9 z = b_{2}$
$- 2 x + 2 y - 6 z = b_{3}$

Dolly Robinson 2020-12-24

Given n>1 , show that the set of all $1 \times n$ matrices of positive integers in countable.

waigaK 2020-12-24

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $[\begin{matrix} 1 & - 2 & 0 & 0 & - 3 \\ 0 & 0 & 1 & 0 & - 4 \\ 0 & 0 & 0 & 1 & 5 \end{matrix}]$

ringearV 2020-12-22

The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or $x_{1}, x_{2}, x_{3}, x_{4}$
(b) Determine whether the system is consistent. If it is consistent, give the solution.
$\begin{matrix} 1 & 0 & 3 & 0 & 1 \\ 0 & 1 & 4 & 3 & 2 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}$

Khadija Wells 2020-12-21

If A and B are $n \times n$ matrices. Find the cost of calculating $A^{2} + B A B$

texelaare 2020-12-21

Enter the expression that would produce the answer (do include the answer) for row 1 column 1 of the multiplied matrix $A \cdot B$ :
List the expression in order with the original values using $\cdot$ for multiplication.
then find $A \cdot B$
If $A = [\begin{matrix} 3 & 7 \\ 2 & 4 \end{matrix}] and B = [\begin{matrix} - 3 & 6 \\ 4 & - 2 \end{matrix}]$

Khaleesi Herbert 2020-12-21

Find the inverse of each of the following matrices.
$[\begin{matrix} 3 & 0 \\ 9 & 3 \end{matrix}]$

CheemnCatelvew 2020-12-21

Construct a $4 \times 3$ matrix with rank 1

Dolly Robinson 2020-12-17

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) Addition of matrices is not commutative.
(b) The transpose of the sum of matrices is equal to the sum of the transposes of the matrices.

Jaden Easton 2020-12-16

Consider the matrices
$A = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}], B = [\begin{matrix} 2 & 3 \\ 1 & 5 \end{matrix}], C = [\begin{matrix} 1 & 0 \\ 0 & 8 \end{matrix}], D = [\begin{matrix} 2 & 0 & - 1 \\ 1 & 4 & 3 \\ 5 & 4 & 2 \end{matrix}] and F = [\begin{matrix} 2 & - 1 & 0 \\ 0 & 1 & 1 \\ 2 & 0 & 3 \end{matrix}]$
a) Show that A,B,C,D and F are invertible matrices.
b) Solve the following equations for the unknown matrix X.
(i) $A X^{T} = B C^{3}$
(ii) $A^{- 1} (X - T)^{T} = (B^{- 1})^{T}$
(iii) $X F = F^{- 1} - D^{T}$

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