Matrices and Systems of Linear Equations

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

These matrices are being multiplied. Determine the dimension/size of the new matrix. 

• Can't multiply them
• 4  x  2
• 3  x  3
• 4  x  3

What is the purpose of row operations in solving augmented matrices?

• To create a new matrix

• To find the determinant of the matrix

• To calculate the inverse of the matrix

• To simplify and solve the system of equations.

What are the three row operations used to solve augmented matrices?

• Interchange two rows, Multiply a row by a non-zero constant, Add a multiple of one row to another row

• Swap two rows

• Divide a row by a non-zero constant

• Subtract a multiple of one row from another row

What in the answer matrix indicates that there is an infinite number of solutions, infinitely many solutions?

• the first part of the solution matrix will look like the identity matrix

• The solution matrix will be a square matrix

• One of the rows in the solution matrix will have all zeros

• One of the rows in the solution matrix will have zeros and 1 number.

What in the answer matrix indicates that there is no solution?

• the first part of the solution matrix will look like the identity matrix

• The solution matrix will be a square matrix

• One of the rows in the solution matrix will have all zeros

• One of the rows in the solution matrix will have zeros and 1 number.

Reduced Row Echelon Form is where ______________________

• Zeroes in the first column of my matrix

• Thel ast column has all zeroes

• One's are in a diagonal pattern of my matrix with zeroes underneath the one's.before the augmented portion

• One's are in a diagonal pattern of my matrix with zeroes above and below the ones before the augmented portion

What is the difference between row echelon form and reduced row echelon form?

• The row echelon form allows for leading coefficients other than 1.

• The reduced row echelon form does not require the leading coefficient to be 1.

• The difference between row echelon form and reduced row echelon form is that the reduced row echelon form has the additional condition that the leading coefficient of each nonzero row is always 1.

• The row echelon form has more strict conditions for zero rows than the reduced row echelon form.

This is an example of

• Row Echelon Form

• Reduced Row Echelon Form

• Really Reduced Echelon Form

• Really Really Easy Form

This is an example of a

• System of Quadratic Equations

• Reduced Row Echelon Form

• Augmented Matrix

• A Canine Doing a Backflip