Matrices: Understanding Systems of Equations with Examples

Simplify
1) $[\begin{matrix} 4 & 5 \end{matrix}] + [\begin{matrix} 6 & - 4 \end{matrix}]$
2) $[\begin{matrix} 4 & - 1 \\ 3 & 3 \\ - 5 & - 4 \end{matrix}] - [\begin{matrix} 4 & - 2 \\ 3 & 6 \\ - 5 & - 6 \end{matrix}]$
3) $[\begin{matrix} 4 & - 1 \\ 6 & - 3 \end{matrix}] + [\begin{matrix} 5 & - 6 \\ 5 & - 5 \end{matrix}] - [\begin{matrix} - 2 & 0 \\ - 2 & - 6 \end{matrix}]$
Solve for x and y
$[\begin{matrix} - 10 & - 4 \\ x & - 1 \end{matrix}] + [\begin{matrix} - 5 & 8 \\ y & - 10 \end{matrix}] = [\begin{matrix} - 15 & x \\ 16 & - 11 \end{matrix}]$

tabita57i 2021-02-09

Given:
$A = [[- 2, 3], [0, 1]]$
$B = [[8, 1], [5, 4]]$
Find the following matrices:
a. A + B
b. A - B
c. -4A
d. 3A + 2B.

Lewis Harvey 2021-02-09

verify that (AB)C = A(BC)
If $A = [\begin{matrix} 2 & 4 \\ 1 & 3 \end{matrix}], B = [\begin{matrix} - 2 & 1 \\ 0 & 4 \end{matrix}], C = [\begin{matrix} 3 & 1 \\ 2 & 1 \end{matrix}]$

DofotheroU 2021-02-09

Write the matrix equation as a system of linear equations without matrices.
$[\begin{matrix} 2 & 0 & - 1 \\ 0 & 3 & 0 \\ 1 & 1 & 0 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 6 \\ 9 \\ 5 \end{matrix}]$

Reggie 2021-02-09

find which of the given matrices are nonsingular.
a) $[\begin{matrix} 1 & 2 & - 3 \\ - 1 & 2 & 3 \\ 0 & 8 & 0 \end{matrix}]$
b) $[\begin{matrix} 1 & 2 & - 3 \\ - 1 & 2 & 3 \\ 0 & 1 & 1 \end{matrix}]$
c) $[\begin{matrix} 1 & 1 & 2 \\ - 1 & 3 & 4 \\ - 5 & 7 & 8 \end{matrix}]$
d) $[\begin{matrix} 1 & 1 & 4 & - 1 \\ 1 & 2 & 3 & 2 \\ - 1 & 3 & 2 & 1 \\ - 2 & 6 & 12 & - 4 \end{matrix}]$

generals336 2021-02-09

1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?

zi2lalZ 2021-02-09

Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

babeeb0oL 2021-02-09

Verify if the statement is true: The eigenvalues of a linear transformation T in L(U) are independent of the chosen base of U.

SchachtN 2021-02-08

Determine whether each statement is sometimes, always , or never true for matrices A and B and explain your reasoning. Stuck on one of them? Try a few examples.
1) If A+B exists , then A-B exists
2) If A and B have the same number of elements , then A+B exists.

Josalynn 2021-02-08

Let A be a $n x x n$ matrix and let
$B = A + A^{T} a n d C = A - A^{T}$
(a) Show that B is symmetric and C is skew symmetric.
(b) Show that every n × n matrix can be represented as a sum of a symmetric matrix and a skew-symmetric matrix.

ruigE 2021-02-08

simplify the following matrix expression:
$[\begin{matrix} 1 & 5 \\ 2 & - 3 \\ - 3 & 7 \end{matrix}] - 2 [\begin{matrix} 2 & - 3 \\ 8 & 5 \\ - 1 & - 1 \end{matrix}] = ?$

Mylo O'Moore 2021-02-08

Let $M_{2 \times 2} (Z / 6 Z)$ be the set of 2 x 2 matrices with the entries in $Z / 6 Z$
a) Can you find a matrix $M_{2 \times 2} (Z / 6 Z)$ whose determinant is non-zero and yet is not invertible?
b) Does the set of invertible matrices in $M_{2 \times 2} (Z / 6 Z)$ form a group?

ringearV 2021-02-08

Use elementary matrices to write ? in row reduced echelon form. Use the elementary matrices to find the inverse of
$A = [\begin{matrix} 1 & 0 & - 2 \\ 0 & 2 & 1 \\ 0 & 0 & 1 \end{matrix}]$

Kaycee Roche 2021-02-08

Use matrices to solve the given system of equations. Use back-substitution Gaussian elimination or Gauss-Jordan elimination.
${\begin{cases} x + 3 y = 0 \\ x + y + z = 1 \\ 3 x - y - z = 11 \end{cases}$

Josalynn 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Phoebe 2021-02-06

Let the matrix A,B, C and D be as given. Find the product of the sum of A and B and the difference between C and D.
$A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}], B = [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}], C = [\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}], D = [\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$

tricotasu 2021-02-06

Add the following matrices. $[\begin{matrix} - 4 & - 4 \\ 5 & - 1 \\ - 3 & 1 \end{matrix}], [\begin{matrix} 0 & 0 \\ 3 & 1 \\ - 4 & 1 \end{matrix}]$

lwfrgin 2021-02-05

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. $A = [\begin{matrix} 1 & 2 & 3 & 4 \end{matrix}], B = [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$

smileycellist2 2021-02-05

Solve the systems of equations using matrices.
$4 x + 5 y = 8$
$3 x - 4 y = 3$
Leave answer in fraction form.
$4 x + y + z = 3$
$- x + y = - 11 + 2 z$
$2 y + 2 z = - 1 - x$

banganX 2021-02-05

$A = [\begin{matrix} 2 & 1 & 1 \\ - 1 & - 1 & 4 \end{matrix}] B = [\begin{matrix} 0 & 2 \\ - 4 & 1 \\ 2 & - 3 \end{matrix}] C = [\begin{matrix} 6 & - 1 \\ 3 & 0 \\ - 2 & 5 \end{matrix}] D = [\begin{matrix} 2 & - 3 & 4 \\ - 3 & 1 & - 2 \end{matrix}]$
a) $A - 3 D$
b) $B + \frac{1}{2}$
c) $C + \frac{1}{2} B$
(a),(b),(c) need to be solved

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