Matrices - plase help!

Deadbot-22

Right so I've an exam tomorrow on Matrices and Vectors and I haven't a clue how to answer the following questions. Any help with them would be much appreciated.

Question 1 - The reduced row-echelon forms of the following augmented matrices systems are given below. How many solutions does each system have.



Question 2 - Assume A and B are 5x3-matrices and C is a 6x5-matrix. Find out which of the following operations are defined, and determine the size of the resulting matrix.

(i) Ct (ii) CA (iii) C + A (iv) A - B


Thanks in advance!

For the first part: do you know how to describe solution sets of sets of linear equations?

Edit: also, I can't exactly remember how, but can't you determine the number of solutions of a matrix of linear equations in its reduced row echelon form by examining the position and number of free variables?

Second part: there are certain conditions on how you can multiply matrices. For example, you can multiply a nxm matrice by a mxk matrice, but not the other way around. The number of columns of the first matrice to be multiplied has to match the number of rows of the second matrice to be multiplied. As for the addition part, to add matrices they have to be of the same dimension, i.e. both nxm matrices.

LeixlipRed

Hmmm, you need to be very careful how you interpret those original matrices. If the last column is the constant terms of a system of linear equations then that effects things. Normally a dotted line would indicate so. The lack of one could indicate that these are just coefficient matrices which again changes the interpretation. Could you clarify that for us OP?

Deadbot-22

-JammyDodger- wrote: »

For the first part: do you know how to describe solution sets of sets of linear equations?

Edit: also, I can't exactly remember how, but can't you determine the number of solutions of a matrix of linear equations in its reduced row echelon form by examining the position and number of free variables?

Second part: there are certain conditions on how you can multiply matrices. For example, you can multiply a nxm matrice by a mxk matrice, but not the other way around. The number of columns of the first matrice to be multiplied has to match the number of rows of the second matrice to be multiplied. As for the addition part, to add matrices they have to be of the same dimension, i.e. both nxm matrices.

LeixlipRed wrote: »

Hmmm, you need to be very careful how you interpret those original matrices. If the last column is the constant terms of a system of linear equations then that effects things. Normally a dotted line would indicate so. The lack of one could indicate that these are just coefficient matrices which again changes the interpretation. Could you clarify that for us OP?

Yeah I think they're just coefficient matrices as you say.

JammyDodger, think I know what you mean about the free variables, I'll look into that.

Thanks for the help guys.

radio_protector

I would help if i could but i failed matrices and vectors TWICE last year!

->

henbane

In Q1, they're described as augmented matrices systems. That would lead me to believe the solutions to the equations are contained within the matrices.

If I'm right, you need to account for the first variable in the first system & the third row of the second system leads to the answer.

For Q2, only matrices of the same size can be added. For multiplication the number of columns of the first matrix must equal the number of rows in the second matrix. Any matrix can be multiplied by a constant.

Deadbot-22

henbane wrote: »

In Q1, they're described as augmented matrices systems. That would lead me to believe the solutions to the equations are contained within the matrices.

If I'm right, you need to account for the first variable in the first system & the third row of the second system leads to the answer.

For Q2, only matrices of the same size can be added. For multiplication the number of columns of the first matrix must equal the number of rows in the second matrix. Any matrix can be multiplied by a constant.

Thanks!

ZorbaTehZ

You can see from the first one that it has infinite solutions, but the second one has no solutions since the third row implies 0=1.

Deadbot-22

ZorbaTehZ wrote: »

You can see from the first one that it has infinite solutions, but the second one has no solutions since the third row implies 0=1.

Makes sense alright, thanks.