Which of the following are true? (1) The sum of two invertible matrices is invertible (2)...

Which of the following are true?

(1) The sum of two invertible matrices is invertible

(2) The determinant of the sum is the sum of the determinants

(3) The determinant of the inverse is the reciprocal of the determinant

(4) An nxn matrix is invertible if and only if its determinant is zero

(5) The product of two invertible matrices is invertible (so long as the product is defined)

(6) If A is a diagonal 3x3 matrix [a,0,0;0,b,0;0,0,c] then its determinant is the product of its diagonal entries

(7) The union of two subspaces is a subspace

(8) The intersection of two subspaces is a subspace

(9) The set of solutions [x,y,z,u,v] to the equations 3x + 4y + 5z + u + 3v = 12 and 4x + y + z + u - v = 13 form a vector space

(10) If V is a vector space of polynomials and p and q are in V then the product pq is also in V

(11) If V is a subspace of R^3 and w is a vector in v then whenever the dot product w dot u = 0, u must also be in the subspace V

(matrices are written as e.g. [a,b,c; d,e,f; g,h,i; j,k,l] to mean the matrix whose first row is [a,b,c], whose second row is [d,e,f] whose third row is [g,h,i] and whose fourth row is [j,k,l].)

Expert Solution

milcah answered 2 years ago

Two square matrices A and B are called similar if there exists an invertible matrixV suchthatB=V−1AV....

Two square matrices A and B are called similar if there exists an invertible matrixV suchthatB=V−1AV. (a) Explain in detail how similarity is related to the change of basis for- mula. What does similarity imply about the geometric relationship between B and A?

Write a C++ program to determine the sum of two 1-D matrices: A = [a b...

Write a C++ program to determine the sum of two 1-D matrices: A = [a b c d] B = [e f g h] The user will provide the values of a to h.

EXAMPLE 5: FINDING THE SUM AND DIFFERENCE OF TWO 3 X 3 MATRICES

Given A and BMath output errorBBFind the sum.Find the difference. Math output errorA=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]\text{ and }B=\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]A=⎣⎡2144−1012−2−2102⎦⎤ and B=⎣⎡60−510−122−2−4−2⎦⎤

Group theory Consider the group GL2(Zp) of invertible 2X2 matrices with entries in the field Zp,...

Group theory Consider the group GL2(Zp) of invertible 2X2 matrices with entries in the field Zp, where p is an odd prime. Zp is an abelian group under addition, the group of unites of Zp is Zpx, which is an abelian group under multiplication. We say (Zp , +, ·) is a field. Show that the subset D2(Zp) of diagonal matrices in GL2(Zp) is an abelian subgroup of order (p - 1)2. For A, B ∈GL2(Zp), show that A and...

a. Using Matlab scripts create the following matrices (???1 and ???2) ???1 = [ 3 2...

a. Using Matlab scripts create the following matrices (???1 and ???2) ???1 = [ 3 2 −3 6 7 4 3 −6 7 ], ???2 = [ 2 1 7 3 3 9 −6 6 1 ] b. Write code to add the second row of ???1 to the third row of ???2 and store results in the first row of ???1. c. Write code to add the second column of ???1 with the third column of ???2 and...

1. TRUE OR FALSE: In general, the sum of alpha and beta should equal 1. 2....

1. TRUE OR FALSE: In general, the sum of alpha and beta should equal 1. 2. TRUE OR FALSE: The most common power level is .05. 3. Which hypothesis states that there will be an effect, difference or association? A. the null B. the alternative C. the alternate D. the nil 4. Which is true of one-tailed tests? A. larger CV B. larger alpha C. less power D. smaller CV 5. TRUE OR FALSE: Failing to find an effect that...

1. All mutations are harmful. a) True b) False 2. Which of the following is TRUE...

1. All mutations are harmful. a) True b) False 2. Which of the following is TRUE about mutations? a) Mutations are more likely to occur if they result in a useful trait b) Mutations can be inherited. c) Mutations only occur during DNA replication d) Mutations do not occur in organisms that reproduce asexually 3. Which of the following would increase the chances of getting a mutation? a) Wearing a hat outside b) Putting sunscreen on your face and arms...

2. a) Find the true value of the probability that the sum of the numbers on...

2. a) Find the true value of the probability that the sum of the numbers on their faces will be at least 2 times 3 when a pair of dice is rolled 162 times b)Find the approximate value of the probability that the sum of the numbers on their face is at least 2 times 3 when a pair of dice is rolled 162 times

1. Proveif ?∈?,then1+(−1)!(2?−1)is a multiple of four 2. If?={∅,{∅}}, which of the following statements is true:...

1. Proveif ?∈?,then1+(−1)!(2?−1)is a multiple of four 2. If?={∅,{∅}}, which of the following statements is true: a.∅⊆? b.{∅}⊆? c.{∅}∈? 3. Provide a grammar for all bit strings that start with exactly one zero followed by even number of 1’s.

Write a function named "check_matrix" which takes two matrices as parameters and returns 1 if the...

Write a function named "check_matrix" which takes two matrices as parameters and returns 1 if the matrices are same or 0 otherwise. Set appropriate parameters and return type if necessary.

Question