Matrices: Understanding Systems of Equations with Examples

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

Yulia 2021-02-23

Given the matrices $A = [\begin{matrix} - 4 & - 3 & 2 \\ 0 & 2 & - 2 \end{matrix}] and B = [\begin{matrix} 0 & - 1 & 5 \\ 2 & - 1 & 2 \end{matrix}]$ A+B=?

Kaycee Roche 2021-02-22

Reduce the following matrices to row echelon form and row reduced echelon forms:
$(i) [\begin{matrix} 1 & p & - 1 \\ 2 & 1 & 7 \\ - 3 & 3 & 2 \end{matrix}] (i i) [\begin{matrix} p & - 1 & 7 & 2 \\ 2 & 1 & - 5 & 3 \\ 1 & 3 & 2 & 0 \end{matrix}]$
Find also the ra
of these matrices.
Notice: $p = 4$

Jaya Legge 2021-02-21

Determine the null space of each of the following matrices:
$[\begin{matrix} 1 & 1 & - 1 & 2 \\ 2 & 2 & - 3 & 1 \\ - 1 & - 1 & 0 & - 5 \end{matrix}]$

Bevan Mcdonald 2021-02-21

A,B,C are $3 \times 3$ matrices with det(A)=-3 , det(D)=-2, det(C)=6.What is $d e t (A^{T} A^{- 1})$ ?
1
-9
3
-1
9

Albarellak 2021-02-21

Let A,B be two matrices with linearly independent columns . If $C o l (A) = C o l (B)$ then $A (A^{T} A)^{- 1} A^{T} = B (B^{T} B)^{- 1} B^{T}$
True or False?

Kaycee Roche 2021-02-20

Compute the product AB by the definition of the product of matrices, where $A b_{1} and A b_{2}$ are computed separately, and by the row-column rule for computing AB.
$A = [\begin{matrix} - 1 & 2 \\ 2 & 5 \\ 5 & - 3 \end{matrix}], B = [\begin{matrix} 4 & - 1 \\ - 2 & 4 \end{matrix}]$
Determine the product AB
AB=?

glasskerfu 2021-02-20

Derive the matrix that represents a pure rotation about the (i) y-axis , (ii) z-axis and (iii) x-axis of the reference frame with the help of diagram.

allhvasstH 2021-02-19

If 4A-3B=2C (where A,B and C are all matrices) then Matrix A can be defined as:
Select one:
a) 0.5C+3B
b) $\frac{2 C + 3 B}{4}$
c) 0.5C+0.75B
d) C+B

Tammy Todd 2021-02-19

Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then $A B = B A$

floymdiT 2021-02-16

If $3 [\begin{matrix} x_{1} & x_{2} \\ x_{3} & x_{4} \end{matrix}] = [\begin{matrix} x_{1} & 2 \\ - 1 & 4 x_{4} \end{matrix}] + [\begin{matrix} 4 & x_{1} + x_{2} \\ x_{3} + x_{4} & 3 \end{matrix}]$
1. $x_{1} = - 2, x_{2} = 2, x_{3} = - 2, x_{4} = - 3$
2. $x_{1} = 2, x_{2} = - 2, x_{3} = - 2, x_{4} = - 3$
3. $x_{1} = 2, x_{2} = 2, x_{3} = 2, x_{4} = - 3$
4. $x_{1} = 2, x_{2} = 2, x_{3} = - 2, x_{4} = 3$
5, $x_{1} = 2, x_{2} = 2, x_{3} = - 2, x_{4} = - 3$

Cabiolab 2021-02-15

Given the two matrices,
$A = [\begin{matrix} 1 & 2 & 3 \\ 1 & 1 & 2 \\ 0 & 1 & 2 \end{matrix}] and B = [\begin{matrix} 1 & 1 & 1 \\ 2 & 1 & 2 \\ 3 & 1 & 2 \end{matrix}]$
(a) Find det A, det B , det(AB) , det(BA) , det(5A) , $d e t A^{T}$ and $d e t (B^{6})$
(b) Find adj A and adj B
(c) Find $A^{- 1}$ and $B^{- 1}$ using the adjoint matrices you found in part (b)

Josalynn 2021-02-14

Prove the following
A(rB)= r(AB)= (rA)B
where r and s are real numbers and A and B are matrices

illusiia 2021-02-14

Prove that if A has rank r with r > 0, then A has an r×r invertible submatrix.

Reggie 2021-02-14

Let $A = [\begin{matrix} 1 & 2 & - 1 \\ 1 & 0 & 3 \\ 1 & 1 & - 1 \end{matrix}]$
i) Find the determinant of A
ii)Verify that the matrix
$[\begin{matrix} - \frac{3}{4} & \frac{1}{4} & \frac{6}{4} \\ 1 & 0 & - 1 \\ \frac{1}{4} & \frac{1}{4} & - \frac{1}{2} \end{matrix}]$ is the inverse matrix of A

Globokim8 2021-02-14

An industrial system with three industries has the input-output matrix D and external demand matrix E below. Solve for the output matrix X in the equation
X = DX + E.
$D = [\begin{matrix} 0.1 & 0.3 & 0.2 \\ 0.0 & 0.2 & 0.3 \\ 0.4 & 0.1 & 0.1 \end{matrix}] and E = [\begin{matrix} 3000 \\ 3500 \\ 8500 \end{matrix}]$

djeljenike 2021-02-13

Describe how to multiply matrices.

Kaycee Roche 2021-02-13

Solve the system of linear equations using matrices.
x+y+z=3
2x+3y+2z=7
3x-4y+z=4

snowlovelydayM 2021-02-12

For which values of the constants c and d is $[\begin{matrix} 5 \\ 7 \\ c \\ d \end{matrix}]$ a linear combination of $[\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}] and [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$

ankarskogC 2021-02-12

Write the uncoded row matrices for the message.
Message: SELL CONSOLIDATED
Row Matrix Size: $1 \times 3$
Encoding Matrix: $A = [\begin{matrix} 1 & - 1 & 0 \\ 1 & 0 & - 1 \\ - 6 & 3 & 2 \end{matrix}]$
SEL= $[\begin{matrix} 19 & 5 & 12 \end{matrix}]$
L-C= $[\begin{matrix} 12 & 0 & 3 \end{matrix}]$
ONS= $[\begin{matrix} 15 & 14 & 19 \end{matrix}]$
OLI= $[\begin{matrix} 15 & 12 & 9 \end{matrix}]$
DAT= $[\begin{matrix} 4 & 1 & 20 \end{matrix}]$
ED= $[\begin{matrix} 5 & 4 & 0 \end{matrix}]$

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