91Ó°ÊÓ

Comparing Solutions of Two Systems In, determine whether the two systems of linear equations yield the same solution. If so, find the solution using matrices. $$(a)\left\\{\begin{array}{rrr}{x+3 y-z=} & {19} \\ {y+6 z=} & {-18} \\ {z=} & {-4}\end{array}\right.$$ $$(b)\left\\{\begin{array}{rrr}{x-y+3 z=} & {-15} \\ {y-2 z=} & {14} \\ {z=} & {-4}\end{array}\right.$$

Curve Fitting, use a system of equations to find the quadratic function \(f(x)=a x^{2}+b x+c\) that satisfies the given conditions. Solve the system using matrices. $$f(1)=1, f(2)=-1, f(3)=-5$$

True or False? In Exercises 95 and 96, determine whether the statement is true or false. Justify your answer If a square matrix has an entire row of zeros, then the determinant will always be zero.

Curve Fitting, use a system of equations to find the quadratic function \(f(x)=a x^{2}+b x+c\) that satisfies the given conditions. Solve the system using matrices. $$f(1)=2, f(2)=9, f(3)=20$$

True or False? In Exercises 95 and 96, determine whether the statement is true or false. Justify your answer If two columns of a square matrix are the same, then the determinant of the matrix will be zero.

Curve Fitting, use a system of equations to find the quadratic function \(f(x)=a x^{2}+b x+c\) that satisfies the given conditions. Solve the system using matrices. $$f(-2)=-15, f(-1)=7, f(1)=-3$$

True or False? In Exercises 95 and 96, determine whether the statement is true or false. Justify your answer Providing a Counterexample Find square matrices \(A\) \(|A+B| \neq|A|+|B|\)

Conjecture Consider square matrices in which thh entries are consecutive integers. An example of such a matrix is $$\left[ \begin{array}{rrr}{4} & {5} & {6} \\ {7} & {8} & {9} \\ {10} & {11} & {12}\end{array}\right]$$ (a) Use a graphing utility to evaluate the determinants of four matrices of this type. Make a conjecturebased on the results. (b) Verify your conjecture.

Curve Fitting, use a system of equations to find the quadratic function \(f(x)=a x^{2}+b x+c\) that satisfies the given conditions. Solve the system using matrices. $$f(-2)=-3, f(1)=-3, f(2)=-11$$

Writing Write a brief paragraph explaining the difference between a square matrix and its determinant.