Answer to Question #298046 in Linear Algebra for Pheeha

Question

1.Which of the following is a linear equation in x,yand z?

1. -x–¹ + e–√²y=3z l, where e= 2.71828

2. 2πln(e–½) - 2y + z= ln(3) - x.

3. √y² + 4y - 2z = 7x.

4.y + 4y - 2z = 7x–².

2.Solve for X from the matrix equation below. Here is the identity matrix and det(A) ≠ 0.

A²X + l = AB

Choose the correct option:

1. X is the identity matrix.

2. X= A–¹B - l

3. X= A–¹B + l

4. X= A–¹B - A

5. X= AB + B

Answer 1

1. If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then $ax + by + cz = r$ is called a linear equation in three variables.

Then answer is

2.

3.

2.

$$A^2X+I=AB$$

$$A^{-1}AAX+A^{-1}I=A^{-1}AB$$

$$AX+A^{-1}=B$$

$$A^{-1}AX+A^{-1}A^{-1}=A^{-1}B$$

$$X=A^{-1}B-A^{-1}A^{-1}$$

We cannot choose the correct option.