Mark each statement True or False. Justify

Chapter , Problem 1E

(choose chapter or problem)

Problem 1E

Mark each statement True or False. Justify each answer. Assume that all matrices here are square.

a. If A is a 2 × 2 matrix with a zero determinant, then one column of A is a multiple of the other.

b. If two rows of a 3 × 3 matrix A are the same, then det A = 0.

c. If A is a 3 × 3 matrix, then det 5A = 5 det A.

d. If A and B are n × n matrices, with det A = 2 and det B = 3, then det.(A + B) = 5.

e. If A is n × n and det A = 2, then det A3 = 6.

f. If B is produced by interchanging two rows of A, then det B = det A.

g. If B is produced by multiplying row 3 of A by 5, then det B = 5 · det A.

h. If B is formed by adding to one row of A a linear combination of the other rows, then det B = det A.

i.   det

j.  det    

k.  det

l. Any system of n linear equations in n variables can be solved by Cramer’s rule.

m. If u and v are in  then the area of the triangle in the plane with vertices at 0, u, and v is 10.

n.  If = 0.

o.  If

p.  If