0
Add your answer:
Earn +20 pts
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.
What does S R followed by a number mean?
If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.
What is the power of a product under law exponent?
alam nyo b yung law for powerof a product
What is the largest number under 100 that is the product of 2 primes numbers?
95 is the product of two primes, 5 and 19.
Is the product of an even number and an even number closed under multiplication?
Yes.
What is the typical lifetime of this product?
This product is pretty sturdy and it will last forever under the proper condition.
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.
What is order of the resultant matrix AB when two matrices are multiplied and the order of the Matrix A is m n order of Matrix B is n p Also state the condition under which two matrices can be mult?
the order is m p and the matrices can be multiplied if and only if the first one (matrix A) has the same number of columns as the second one (matrix B) has rows i.e)is Matrix A has n columns, then Matrix B MUST have n rows.Equal Matrix: Two matrices A=|Aij| and B=|Bij| are said to be equal (A=B) if and only if they have the same order and each elements of one is equal to the corresponding elements of the other. Such as A=|1 2 3|, B=|1 2 3|. Thus two matrices are equal if and only if one is a duplicate of the other.
How are the inverse matrix and identity matrix related?
If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
What is a unique name under which a product is marketed?
product name
How does product advertising differ from institutional advertising under what conditions will they be used?
How does product advertising differ from institutional advertising under what conditions will they be used?How does product advertising differ from institutional advertising under what conditions will they be used?
What are the conditions under which a force does no work?
A force does no work when there is no displacement of the object it is acting on, or when the force is perpendicular to the direction of motion. Another condition is when the force applied is zero, since work is the product of force and displacement.
What is the decision making under certainty condition?
decition making under certainty
In Florida what is a sea or mining product?
Amining product is a product found under ground
What does S R followed by a number mean?
If you mean what does something like SL(3, R) mean, it is the group of all 3X3 matrices with determinant 1, with real entries, under matrix multiplication.
Under what condition might an individual be charged under treasonable felony?
Planning a revolution;)
What is a condition in which mites burrow under the skin?
Scabies.
