Question

In: Advanced Math

Consider a square matrix A such that Ker(A2 ) = Ker(A3 ). Is Ker(A3 ) =...

Consider a square matrix A such that Ker(A2 ) = Ker(A3 ). Is Ker(A3 ) = Ker(A4 ). Explain your reasoning.

Solutions

Expert Solution

Let A be a square matrix such that .

Let .

Then,

[matrix multiplication isassociative]

Then,

So,

Now, let .

Then,

[matrix multiplication isassociative]

Since and , then

[matrix multiplication isassociative]

Then,

So,

So, from (1) and (2), .

Colby Messinger answered 2 years ago

Next > < Previous

Related Solutions

covert the schema into 3NF. TableC (a1,a2,a3,a4,a5) functionally dependencies: a1 --> {a2,a3,a5} a4 --> {a1,a2,a3,a5} a3...

covert the schema into 3NF. TableC (a1,a2,a3,a4,a5) functionally dependencies: a1 --> {a2,a3,a5} a4 --> {a1,a2,a3,a5} a3 -->{a5} Answer: Relation1: Relation2:

Let A = {a1, a2, a3, . . . , an} be a nonempty set of...

Let A = {a1, a2, a3, . . . , an} be a nonempty set of n distinct natural numbers. Prove that there exists a nonempty subset of A for which the sum of its elements is divisible by n.

Consider the following eight examples: A1 = (4,20), A2 = (4,10), A3 = (16,8), A4 =...

Consider the following eight examples: A1 = (4,20), A2 = (4,10), A3 = (16,8), A4 = (10,16), A5 = (14,10), A6 = (12,8), A7 = (2,4), A8 = (8,18) The distance function is Euclidian distance. Use single-link, complete-link agglomerative clustering, and centroid techniques to cluster these examples. Show your calculations and draw the dendrograms for each technique.

For each of the following sequences find a functionansuch that the sequence is a1, a2, a3,...

For each of the following sequences find a functionansuch that the sequence is a1, a2, a3, . . .. You're looking for a closed form - in particular, your answer may NOT be a recurrence (it may not involveany otherai). Also, while in general it is acceptable to use a "by cases"/piecewise definition, for this task you must instead present a SINGLE function that works for all cases.(Hint: you may find it helpful to first look at the sequence of...

Alternating Series Test. Let (an) be a sequence satisfying (i) a1 ≥ a2 ≥ a3 ≥...

Alternating Series Test. Let (an) be a sequence satisfying (i) a1 ≥ a2 ≥ a3 ≥ · · · ≥ an ≥ an+1 ≥ · · · and (ii) (an) → 0. Show that then the alternating series X∞ n=1 (−1)n+1an converges using the following two different approaches. (a) Show that the sequence (sn) of partial sums, sn = a1 − a2 + a3 − · · · ± an is a Cauchy sequence Alternating Series Test. Let (an) be...

A company uses three different assembly lines – A1, A2, and A3 – to manufacture a...

A company uses three different assembly lines – A1, A2, and A3 – to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2’s components need rework and 10% of A3’s need rework. Suppose that 50% of all components are produced by line A1, 30% are produced by line A2, and 20% come from line A3. (a) Suppose a component is selected at random, what is the probability that...

Find an arithmetic code for a symbol p4p4p3 for the source alphabet {a1, a2, a3, a4,...

Find an arithmetic code for a symbol p4p4p3 for the source alphabet {a1, a2, a3, a4, a5}, with symbol probabilities p1 = 0.11, p2 = 0.05, p3 = 0.10, p4 = 0.70, and p5 = 0.04. Show the work please.

2. Write the hexadecimal numbers in the registers of $a0, $a1, $a2, $a3 after the following...

2. Write the hexadecimal numbers in the registers of $a0, $a1, $a2, $a3 after the following codes running: ori $a0, $0, 11 ori $a1, $0, 19 addi $a1, $a1, -7 slt $t2, $a1, $a0 beq $t2, $0, label addi $a2, $a1, 0 sub $a3, $a1,$a0 j end_1 label: ori $a2, $a0, 0 add $a3, $a1, $a0 end_1: xor $t2, $a1, $a0 *Values in $a0, $a1, $a2, $a3 after the above instructions are executed.

Suppose that A is an n × n matrix satisfying A3 - 3A + 2A-3l =...

Suppose that A is an n × n matrix satisfying A3 - 3A + 2A-3l = 0. Show that A is invertible by the definition of invertible. (Hint: Review the definition of invertible, and then describe the inverse in terms of the matrix A - you don’t need to know what A is to answer this question.)

Why matrix can be multiplied by itself if and only if it is a square matrix?

Subjects