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Chapter 9: Problem 65

What is meant by the order of a matrix? Give an example with your explanation.

Short Answer

Expert verified
The order of a matrix is given by its dimensions, specifically the number of rows followed by the number of columns. For instance, a matrix with three rows and three columns would have an order of \(3 \times 3\).

Step by step solution

01

Definition of Matrix Order

The order of a matrix is a term used to describe the dimensions of a matrix. It is usually expressed by \(m \times n\) where 'm' is the number of rows and 'n' is the number of columns. Thus, the order of a matrix gives us the exact idea of the size of the matrix.
02

Illustrative Example

For example, consider a matrix \( A = \[ \[ 1, 2, 3 \], \[ 4, 5, 6 \], \[ 7, 8, 9 \] \] \). Here, matrix A has three rows and three columns. Therefore, the order of this matrix is \(3 \times 3\).

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Most popular questions from this chapter

The table shows the daily production level and profit for a business. y (Daily Profit) $$ \begin{array}{ll} {x \text { (Number of Units }} & {30} & {50} & {100} \\ {\text { Produced Daily) }} \\ {y \text { (Daily Profit) }} & {\$ 5900} & {\$ 7500} & {\$ 4500} \end{array} $$ Use the quadratic function \(y=a x^{2}+b x+c\) to determine the number of units that should be produced each day for maximum profit. What is the maximum daily profit?

Find (if possible) the following matrices: a. \(A B\) b. \(B A\) $$ A=\left[\begin{array}{rrrr} {2} & {-3} & {1} & {-1} \\ {1} & {1} & {-2} & {1} \end{array}\right], \quad B=\left[\begin{array}{rr} {1} & {2} \\ {-1} & {1} \\ {5} & {4} \\ {10} & {5} \end{array}\right] $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with two matrices that can be added but not multiplied.

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \left\\{\begin{array}{l} {2 x+2 y+7 z=-1} \\ {2 x+y+2 z=2} \\ {4 x+6 y+z=15} \end{array}\right. $$

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \left\\{\begin{aligned} w+x+y+z &=4 \\ 2 w+x-2 y-z &=0 \\ w-2 x-y-2 z &=-2 \\ 3 w+2 x+y+3 z &=4 \end{aligned}\right. $$
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