Consider only square matrices. True or false? Explain. a) det(AB) = (det A)(det B). b) Eigenvalues...

Consider only square matrices. True or false? Explain.

a) det(AB) = (det A)(det B).

b) Eigenvalues of all real matrices are real.

c) The determinant of an upper triangular matrix is the sum of its main diagonal entries.

Expert Solution

Colby Messinger answered 10 months ago

Consider A, B and C, all nxn matrices. Show that: 1) det(A)=det(A^T) 2) if C was...

Consider A, B and C, all nxn matrices. Show that: 1) det(A)=det(A^T) 2) if C was obtained from A by changing the i-th row (column) with the j-th row (column). Show that det(C)=-det(A) 3) det(AB)=det(A)det(B) 4) Let C be a matrix obtained from A by multiplying a row by c ∈ F. Show that det(B)=c · det(A)

for square matrices A and B show that [A,B]=0 then [A^2,B]=0

1. Find all eigenvalues of each of the following matrices. (a) |10 −18 b) |2 −1...

1. Find all eigenvalues of each of the following matrices. (a) |10 −18 b) |2 −1 (c) |5 4 2 6 −11 | 5 -2| 4 5 2 2 2 2|

An American option may be exercised only at maturity. True or false? True False

True or False. Indicate whether the statement is true or false. If false, explain in the...

True or False. Indicate whether the statement is true or false. If false, explain in the space provided the statement why it is false, or simply correct the statement. Smooth muscle contraction is regulated by the autonomic nervous system. During exercise, the sympathetic nerves that innervate the smooth muscles of bronchioles and arterioles regulate the contraction of these smooth muscles to increase ventilation and cardiac output. 2. Multiple choice: Choose one best statement. An infant born prematurely has neonatal respiratory...

B. Theorems--True or False? For each proposition, considered independently: (a) State whether True or False. (b)...

B. Theorems--True or False? For each proposition, considered independently: (a) State whether True or False. (b) Then explain your answer. Define the important terms in your explanation. You may use graphs in your answers. B1. A country's potential output can increase while its actual output decreases. B2. China will likely surpass the United States in per-capita GDP before it surpasses the United States in GDP itself.

True or False. If false explain why it is false and explain what is meant by...

True or False. If false explain why it is false and explain what is meant by all parts of the statement. The nuclear localization is a post-translational modification.

Explain why the statement is true or false; Affordable bundles for a consumer only include those...

Explain why the statement is true or false; Affordable bundles for a consumer only include those bundles on or below the budget line itself.

Write TRUE if the statement is TRUE. If the statement is FALSE, write FALSE and explain...

Write TRUE if the statement is TRUE. If the statement is FALSE, write FALSE and explain why 3. The Commissioner of Internal Revenue may prescribe presumptive gross sales and receipts for a taxpayer when the latter fails to issue receipts and when he believes that the books or other records of the latter do not correctly reflect declarations in the return. 4. Jurisdiction is the power and authority of the court to hear, try, and decide a case. It can...

1. True or False: Confidence intervals can only be calculated for means. True False SAVE 2....

1. True or False: Confidence intervals can only be calculated for means. True False SAVE 2. Suppose a sample of 200 barrow-wights (wraith-like creatures that feed on the life force of the living) yields a sample mean of 6.2 living beings consumed per day. Assuming a standard error of 1.7, what would the upper bound of a 95% confidence interval be? SAVE 3. Using the same ridiculous survey data from the previous question, what would the lower bound of a...

Question