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Chapter 4: Q1. (page 192)

Describe the condition that must be met in order to use Cramer’s rule.

Short Answer

Expert verified

The required condition is that the denominator should not be 0.

Step by step solution

01

Step 1- Determine the factor that is related to the required condition

Determinant plays a major role for the application of Cramer’s rule as all the calculations are done through determinants.

02

– Analyze the obtained factor

The numerator and denominator of the value of each variable related to the determinants and if that determinant becomes 0 then the Cramer’s rule will not applicable in any circumstances.

03

Step 3- Make the conclusion

The required condition is that the denominator should not be 0.

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Most popular questions from this chapter

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

21. $8 [\begin{matrix} 0.25 & 0.5 \\ 0.75 & 1.5 \end{matrix}] - 2 [\begin{matrix} 0.25 & 0.5 \\ 0.75 & 1.5 \end{matrix}]$

State the dimensions of each matrix.

11. $[\begin{matrix} 7 \\ 8 \\ 9 \end{matrix}]$

Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

25. $D - B$

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region.

$\begin{matrix} y \geq \frac{1}{3} x \\ y \geq - 5 x + 16 \\ y \leq - x + 10 \\ f (x, y) = 5 x - y \end{matrix}$

Find the value of each expression.

$- 2 - 8$

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