An overdetermined system is a system of linear equations in which there are more equations than unknowns. This means that there is more information available than needed to solve the system.

Let's analyze each system:

1. 3a+b−6c=−10, 2a+b−5c=−8: This system has 2 equations and 3 unknowns (a, b, c). It is not overdetermined.

2. 2x+y+3z=1, 2x+6y+8z=3, 6x+8y+18z=5: This system has 3 equations and 3 unknowns (x, y, z). It is not overdetermined.

3. p+q=1, p+q+r=2, p−q+r=1, p−r=3: This system has 4 equations and 3 unknowns (p, q, r). It is overdetermined.

4. 6a+8b+7c+3d=7, 3a+5b+4c+d=8: This system has 2 equations and 4 unknowns (a, b, c, d). It is not overdetermined.

5. x−y=2, x+y=4, 2x+y=8: This system has 3 equations and 2 unknowns (x, y). It is overdetermined.

So, the overdetermined systems are the third and the fifth.

Question

An overdetermined system is a system of linear equations in which there are more equations than unknowns. This means that there is more information available than needed to solve the system.

Let's analyze each system:

1. 3a+b−6c=−10, 2a+b−5c=−8: This system has 2 equations and 3 unknowns (a, b, c). It is not overdetermined.

2. 2x+y+3z=1, 2x+6y+8z=3, 6x+8y+18z=5: This system has 3 equations and 3 unknowns (x, y, z). It is not overdetermined.

3. p+q=1, p+q+r=2, p−q+r=1, p−r=3: This system has 4 equations and 3 unknowns (p, q, r). It is overdetermined.

4. 6a+8b+7c+3d=7, 3a+5b+4c+d=8: This system has 2 equations and 4 unknowns (a, b, c, d). It is not overdetermined.

5. x−y=2, x+y=4, 2x+y=8: This system has 3 equations and 2 unknowns (x, y). It is overdetermined.

So, the overdetermined systems are the third and the fifth.

Knowee AI · Accepted Answer

An overdetermined system is a system of linear equations in which there are more equations than unknowns. This means that there is more information available than needed to solve the system.

Let's analyze each system:

1. 3a+b−6c=−10, 2a+b−5c=−8: This system has 2 equations and 3 unknowns (a, b, c). It is not overdetermined.

2. 2x+y+3z=1, 2x+6y+8z=3, 6x+8y+18z=5: This system has 3 equations and 3 unknowns (x, y, z). It is not overdetermined.

3. p+q=1, p+q+r=2, p−q+r=1, p−r=3: This system has 4 equations and 3 unknowns (p, q, r). It is overdetermined.

4. 6a+8b+7c+3d=7, 3a+5b+4c+d=8: This system has 2 equations and 4 unknowns (a, b, c, d). It is not overdetermined.

5. x−y=2, x+y=4, 2x+y=8: This system has 3 equations and 2 unknowns (x, y). It is overdetermined.

So, the overdetermined systems are the third and the fifth.

Which of the following are overdetermined systems?3a+b−6c=−102a+b−5c=−82x+y+3z=12x+6y+8z=36x+8y+18z=5p+q=1p+q+r=2p−q+r=1p−r=36a+8b+7c+3d=73a+5b+4c+d=8x−y=2x+y=42x+y=8Submit

Question

Solution

Similar Questions

Upgrade your grade with Knowee