1,954 Answered Questions for the topic linear algebra

Linear Algebra Complex Numbers

10/23/20

determine the complex solutions of the equation

(z+4)3 = -8i
Linear Algebra Complex Numbers

10/23/20

determine the complex solutions of the equation

(z+4)3 = -8i
Linear Algebra

10/23/20

What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?

What is the area of triangle bounded by the x-axis, the y-axis, and the line y=−4x+4?
Linear Algebra Algebra 1 Geometry

10/22/20

Can you help me create a linear model?

I'm trying to help my son with algebra and he got the following problem. His in the 8th grade, but they are having him do HS algebra and he's having a difficult time.The U.S. population in 1910... more
Linear Algebra Geometry Translation Matrices

10/21/20

Find the matrix that performs this translation.

This problem will walk through the process of rotating by 90 degrees counterclockwise around the point (3, 5). Our strategy for rotation around the point (3, 5) will be to begin with a vector whose... more
Linear Algebra

10/17/20

Find all values of c1 and c2 such that: c1(2, 2, 1) + c2(1,-2,2) = (3,6,0)

Linear Algebra Algebra 1

10/16/20

Proofs for symmetric matrices and skew-symmetric matrices

A square matrix 𝐶C is called skew-symmetric if 𝐶𝑇=−𝐶CT=−C.Let 𝐴A be an 𝑛×𝑛n×n square matrix. Set 𝐵=12(𝐴+𝐴𝑇)B=12(A+AT) and 𝐶=12(𝐴−𝐴𝑇)C=12(A−AT).(a) (4 marks) Show that 𝐵B is a symmetric matrix... more
Linear Algebra

10/14/20

A 3×3 matrix 𝐴 has det(𝐴)=2020. Find det(Adj(𝐴)).

Linear Algebra Math

10/12/20

Math Linear Algebra

Find all values of k for which the vectors[1, 1, 1, 1], [1, 2, 3, k], [1, 4, 9, k^2], [1, 8, 27, k^3]are linearly dependent.
Linear Algebra

10/12/20

An n×n matrix A has a fixed point if there is a vector v in Rn with A*v = v.

1)Show that every such A has at least one fixed point. 2) The identity matrix has infinitely many fixed points. For all arbitrary 2 × 2 matrices A, show that if A has two distinct fixed points v... more
Linear Algebra

10/12/20

Help please! Linear algebra

273 students enrolled in a freshman level chemistry class. By the end of the semester, 6 times the number of students passed as failed. Find the number of students who passed, and the number of... more
Linear Algebra

10/11/20

In the year 1989, an investment was worth $30200. In the year 1996, this investment was worth $35800. What is the value and rate of this investment?

In the year 1989, an investment was worth $30200. In the year 1996, this investment was worth $35800. What is the value and rate of this investment?
Linear Algebra

10/10/20

Linear Algebra Notes and Confusion.

Hi, while reading the beginning of the notes in my linear algebra section I immediately hit a wall of confusion. (I've been googling on this and can't find out how he did this.) In the notes (which... more
Linear Algebra Proofs

10/08/20

Order 8 of the following sentences so that they form a direct proof of the statement: 𝐴 is a square matrix. Prove that if 𝐴2=𝐴, then either 𝐴=𝐼 or 𝐴 is singular.

Order 8 of the following sentences so that they form a direct proof of the statement:A is a square matrix. Prove that if , then either  or  is singular.Options: Let A be an m×n matrix. Assume... more
Linear Algebra Proofs

10/08/20

Order 6 of the following sentences so that they form a proof by CONTRAPOSITIVE of the statement: 𝐴 is a square matrix. Prove that if 𝐴^2=𝐴, then either 𝐴=𝐼 or 𝐴 is singular.

Order 6 of the following sentences so that they form a proof by CONTRAPOSITIVE of the statement: 𝐴 is a square matrix. Prove that if , then either  or  is singular.Options: Let A be an m×n... more
Linear Algebra Proofs

10/08/20

Order 9 of the following sentences so that they form a proof by induction of the statement: 1^2+2^2+3^2+...+𝑛2=𝑛(𝑛+1)(2𝑛+1)/6 for all natural numbers n.

Order 9 of the following sentences so that they form a proof by induction of the statement:12+22+32+...+𝑛2=𝑛(𝑛+1)(2𝑛+1)/6 for all natural numbers n.Options We will proceed by induction to prove... more
Linear Algebra Proofs

10/08/20

Order 8 of the following sentences so that they form a proof by induction of the statement: 2^𝑛>4𝑛 for 𝑛>4.

Order 8 of the following sentences so that they form a proof by induction of the statement: 2n>4n for 𝑛>4.Options: Base Case: n=5 Inductive Hypothesis: Assume 2k>4k LHS: 25=32, RHS:... more
Linear Algebra

10/08/20

Which of the following is my assumption in order to do a proof by CONTRAPOSITIVE?

Consider the following statement: If an m x n matrix A is the zero matrix, then it is made entirely of zeros and makes students happy."Which of the following is my assumption in order to do a proof... more
Linear Algebra Algebra

10/07/20

What is the price per ticket for a student ticket?

A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a... more
Linear Algebra

10/07/20

A is a matrix such that 𝐴^2+3𝐴−𝐼=0. Show that 𝐴 is invertible.

Linear Algebra Algebra 1 Critical Thinking

10/06/20

Algebraic equation

Here it is:Casper has 15 pencils. Kenny has an odd number of more pencils than Casper. If Kenny had the same amount of pencils as Casper, then he would have less than Jones. Jones has 2 1/2 times... more
Linear Algebra

10/06/20

word problems with linear equations

A garden table and a bench cost $843 combined. The garden table costs $57 less than the bench. What is the cost of the bench?

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