[BOŞ_SES] a We define the extent of the matrix in the previous session. The matrix in order emerges quite easily. Because we convert the x y with transformation Then because linear A (x) to the individual, x showing the definition of space We define the matrix of numbers obtained from the conversion of the EIA. We show with these matrix with x matte, x as the product We say we show equal, we noticed that many times. If the right side instead of the usual year The need to find a vector x, then it will go to b. This sets us whether the solution of the equation here. In addition, the solution only if the solution or infinite as we were getting that number. It explains current status of visual expression. We xi we sent a space in a conversion ground transportation space of time can have these x. If this transportation is in the right space for this has come against a x b. If we go to the other end if B in the transport space This is not going to b x can not be found, so there is no solution. Solution in time where we meet with two stops. If you are a single x opposed revenue null space it consists only of x that b. Then there is the only solution. But if there is a zero in the vector space, When we add to this that x reaches b, so there are infinite solutions. As we have demonstrated in this. X If we add a zero from the vector space, The definition of the zero space zero goes on, The set of vectors, linear space created for them. A is a linear transformation by collecting wherein for Before you change the order with x convert Summing the two converts the n equal to b coming, but (n) to be zero (x) we know that equals b. But also the effect of x plus n is coming to b, hence only from b (x) is not A (x) any increase with n, This will also be the only solution only if the zero vector, No, because you can add something, but zero space is not empty, If non-zero vectors in this way You can get the infinite variety of vector and adding, all of which goes to the b, which means that an infinite number of solutions. We see it, here we see visually. The following theorem is also important that we do all we used in the examples: the identification space size, plus the size of the space shuttle was the size of the zero space. This means that you get immediate access to the size of the space the size of a null space. When we came to the column matrix of the matrix which showed the number of independent access to space. If you have only one solution it comes equal to the number of unknowns. Now as we make these equations we have seen that side of the vector, If we add the next matrix b extended we get the matrix, brought here when we added the b, m m plus column when there is a column. If you want to be is in space transportation and this is independent of the column matrix gives the size of the space shuttle, b When we add this to say, if it's side it is increasing in size B is independent of this column, but when we add it to the side b, The more the order of the matrix a column extended matrix If the change means be dependent on others. That means in the space formed by the column. He has time solution. Here we can summarize it in the following table. If the extended range of the matrix that is independent The number of columns in the independent column If there is the same solution. Because B does not increase the number of independent columns in this matrix, so dependent on them, if they depended it means that transportation in the column to create space, then there is a solution. But the extent of this matrix unknowns If that number again our famous theorem Remember if zero-dimensional space will be zero. Therefore, it can have a solution if a new floor space from zero No solution is the only solution. But the order of the matrix is smaller than the number of unknowns, It shows the extent of the definition space of unknown number, the definition of the space is small, then the null space that is the size of one or more large, the null space is not empty. Any time you add a solution to the zero vector space again we see that the solution to be around forever. If we add the usual number of columns on the side of b, If the individual growing number of columns, so this extended The size of the matrix to the range greater than the range, A great because you can already add a B, then B, It means independent of the column. It does not mean that space is created in the column to the mean. This shows that solution. This visual As mentioned in the equation as We determine the order of the matrix solutions. Now here is parsed