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If matrix a is invertible and a b is invertible and a 2b a 3b and a 4b are all invertible how can you prove that a 5b is also invertible?
Wiki User
∙ 15y ago
What is "a 3b"? Is it a3b? or a+3b? 3ab? I think "a3b" is the following: A is an invertible matrix as is B, we also have that the matrices AB, A2B, A3B and A4B are all invertible, prove A5B is invertible. The problem is the sum of invertible matrices may not be invertible. Consider using the characteristic poly?
Wiki User
∙ 15y ago
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What is the order of the matrix films?
There are three Matrix movies: The Matrix, The Matrix Reloaded, and The Matrix Revolutions. There are also a series of short animated films called The Animatrix. All movies on TopRater: toprater.com/en/movies/objects/2867535-the-matrix-1999
What is the story behind the makers of Matrix shampoo?
Arnie Miller, an American hairdresser, founded Matrix shampoo in 1980. Matrix shampoo comes in a variety of products so that it can work on all kinds of hair textures and colors.
Identify the command used to generate all ones in a 4X4 matrix?
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How to find the inverse of a square matrix?
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
What is the movie the matrix about?
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How can you tell if a matrix is invertible?
An easy exclusion criterion is a matrix that is not nxn. Only a square matrices are invertible (have an inverse). For the matrix to be invertible, the vectors (as columns) must be linearly independent. In other words, you have to check that for an nxn matrix given by {v1 v2 v3 ••• vn} with n vectors with n components, there are not constants (a, b, c, etc) not all zero such that av1 + bv2 + cv3 + ••• + kvn = 0 (meaning only the trivial solution of a=b=c=k=0 works).So all you're doing is making sure that the vectors of your matrix are linearly independent. The matrix is invertible if and only if the vectors are linearly independent. Making sure the only solution is the trivial case can be quite involved, and you don't want to do this for large matrices. Therefore, an alternative method is to just make sure the determinant is not 0. Remember that the vectors of a matrix "A" are linearly independent if and only if detA�0, and by the same token, a matrix "A" is invertible if and only if detA�0.
Is the set of all 2x2 invertible matrices a subspace of all 2x2 matrices?
I assume since you're asking if 2x2 invertible matrices are a "subspace" that you are considering the set of all 2x2 matrices as a vector space (which it certainly is). In order for the set of 2x2 invertible matrices to be a subspace of the set of all 2x2 matrices, it must be closed under addition and scalar multiplication. A 2x2 matrix is invertible if and only if its determinant is nonzero. When multiplied by a scalar (let's call it c), the determinant of a 2x2 matrix will be multiplied by c^2 since the determinant is linear in each row (two rows -> two factors of c). If the determinant was nonzero to begin with c^2 times the determinant will be nonzero, so an invertible matrix multiplied by a scalar will remain invertible. Therefore the set of all 2x2 invertible matrices is closed under scalar multiplication. However, this set is not closed under addition. Consider the matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible (in this case, they are both their own inverses). However, their sum is {[0 0], [0 0]}, which is not invertible because its determinant is 0. In conclusion, the set of invertible 2x2 matrices is not a subspace of the set of all 2x2 matrices because it is not closed under addition.
Is a to power of 4 multiplied by b to power of 5 invertible?
Indeterminate. How? a4b5 is the expression instead of equality. Since we are not given the equality of two variables, there is no way to determine whether it's invertible or not. Otherwise, if you are referring "a" and "b" as invertible matrices, then yes it's invertible. This all depends on the details.
What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What is the order of the matrix films?
There are three Matrix movies: The Matrix, The Matrix Reloaded, and The Matrix Revolutions. There are also a series of short animated films called The Animatrix. All movies on TopRater: toprater.com/en/movies/objects/2867535-the-matrix-1999
Why is ash from pokemon dadless?
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What is a zero matrix?
A zero matrix is a matrix in which all of the entries are zero.
What is scalene matrix?
A square matrix is said to be scalene Matrix if it has all principal diagonal elements equal and remaining all
What is zero matrix?
it is the matrix consisting of all 0s
Unlock all levels on enter the matrix?
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How do you find the inverse of A in system of linear equation and matrices?
First, we need to recall that a linear equation does not involve any products or roots of variables. All variables occur only to the first power and do not appear as arguments for trigonometric, logarithmic, or exponential functions. For example, x + √y = 4, y = sin x, and 2x + y - z + yz = 5 are not linear.To solve a system of equations such as3x + y = 52x - y = 3all information required for the solution is emboded in the augmented matrix (imagine that I put those information into a rectangular arrays)3 1 52 -1 3and that the solution can be obtained by performing appropriate operations on this matrix.The matrix of this system linear equations is a square matrix A such as3 12 -1Think this matrix asa bc dTo find an inverse of this square matrix A (2 x 2), we need to find a matrix B of the same size such that AB = I and BA = I, then A is said to be invertible and B is called the inverse of A. If no such a matrix can be found, then A is said to be singular.An invertible matrix has exactly one inverse.A square matrix A is invertible if ad - bc ≠ 0 (where ad - bc is the determinant)The formula of finding the inverse of a square matrix A isA-1 = [1/(ad - bc)][d -b the second row -c a](I'm sorry, I can't draw the arrays)So let's find the inverse of our example.A-1 = [1/(-3 -2)][-1 -1 the second row -2 3] = [-1/-5 -1/-5 the sec. row -2/-5 3/-5] =1/5 1/52/5 -3/5A n x m matrix cannot have an inverse. A n x n matrix may or may not have an inverse.To find the inverse of a n x n matrix we should to adjoin the identity matrix to the right side of A, thereby producing a matrix of the form [A | I]. Then we should apply row opperations to this matrix until the left side is reduced to I. This opperations will convert the right side to A-1, so the final matrix will have the form [I |A-1 ].(There are many other methods how to find the inverse of a n x n matrix, but I can't show them by examples. I am so sorry that I can't be so much useful to you).
What is the definition of zero matrix?
Zero Matrix When all elements of a matrix are zero than the matrix is called zero matrix. Example: A=|0 0 0|
