Quiz 3: System of Linear Equations

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What is the Leading 1? *

1 point

The first element of a row and all entries below it are zeros.

The first non-zero element of a row.

The first non-zero element of a row and all entries below are zeros.

The first element of a row and all entries above are zeros.

The first non-zero element of a row and all entries above are zeros.

Determine whether the equation is linear x+5y-sqrt(2z) = 1 *

1 point

Yes

Find a linear equation in x and y whose solution set is given by equations x = 5+2t, y = t. *

1 point

Find the augmenter matrix for a system x = 1, y = 2, z = 3;

Suppose you are asked to find three real numbers such that the sum of the numbers is 12, the sum of two times the first plus the second plus two times the third is 5, and the third number is more than the first. Describe a system of linear equations.

Which of the following vectors is a solution for the system of linear equations *

1 point

(3,1,1)

(3,-1,1)

(13,5,2)

(17,7,5)

Find the equation for the line of intersection of planes x+2y+3z = 1, 3x-2y+z = 2. *

1 point

x = 1-4t, y = 2+5t, z = t;

x = (1,2,0)+(-4,5,1)t

x = 2+5t, y = 1-4t, z = t

x = (2,1,0)+(5,-4,1)t

x = 3/4-t, y = 1/8-t, z = t

x = (3/4,1/8,0)+(-1,-1,1)t

The RREF form of the system of linear equations has 2 rows and 4 columns. The first two columns have pivots. How many solutions the system has?

1 point

Infinitely Many

Clear selection

All columns of the RREF form, except the one which corresponds to the right-hand side of the system of linear equations, have pivots. How many solutions the system has? *

1 point

Infinitely many

Determine whether the equation is linear x+5y-sqrt(2)z = 1 *

1 point

Yes

Find a linear equation in x and y whose solution set is given by x = t, y = 2t+6 *

1 point

Find the equation for the line of intersection of planes x+y-z = 3, 2x+y+3z = 4. *

1 point

x = 1-4t, y = 2+5t, z = t;

x = (1,2,0)+(-4,5,1)t

x = 2+5t, y = 1-4t, z = t

x = (2,1,0)+(5,-4,1)t

Find the system of linear equations corresponding to the following augmented matrices.

0 points

Describe an elementary row operation that produces B from A, and then describe and elementary row operation that recovers A from B.

1 point

2*R1+R2, -2*R1+R2

2*R1+R2, R1+2*R2

-2*R1+R2, 2*R1+R2

2*R1+R2, -4*R1+R2

Clear selection

Describe an elementary row operation that produces B from A, and then describe and elementary row operation that recovers A from B. *

1 point

2*R1, 1/2*R1

-R2+R1, R2+R1

1/2*R1, 2*R1

R2-R1, R1-R2

The last column of the RREF form, which corresponds to the right-hand side part of a system of linear equations, has a pivot. How many solutions the system has? *

1 point

Infinitely Many

Find the general solution for the system 7x-5y = 3. *

1 point

x = 3/7+5/7t, y = t

x = (3/7,0)+(5/7,1)t

x = 5/7t+3/7

x = (5/7,0)+(3/7,0)t

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