Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

This question provides a sample of 20 data values and requires the calculation of mean, median, and standard deviation. The data are presented as a column so they can be easily copy-pasted into a spreadsheet.

Two column vectors are given, with one entry unknown. Given that the vectors are perpendicular, question is to determine the unknown entry.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.