By: Fitria Khasanah page 1

EXERCISE 1 OF ELEMENTARY LINEAR ALGEBRA

(Get into groups of four or five persons)

Meeting-6

1. In each part suppose that the augmented matrix for a system of linear equations has been

reduced by row operations to given reduced row-echelon form. solve the system.

a.

b.

2. Solve each of the following systems by Gauss-Jordan elimination

a.

b. -2b + 3c = 1

3a + 6b - 3c = -2

6a + 6b + 3c = 5

3. Solve the following homogeneus system of linear equations by any method.

a. 2x – y – 3z = 0

-x + 2y – 3z = 0

x + y + 4z = 0

b. v + 3w – 2x = 0

2u + v – 4w + 3x = 0

2u + 3v + 2w – x = 0

-4u -3v + 5w – 4x= 0

By: Fitria Khasanah page 2

4. For which values of will the following system have no solutions? Exactly one

solution? Infinitely many solutions?

x + 2y – 3z = 4

3x – y + 5z = 2

4x + y + ( z = +2

5. Solve the following system of nonlinear equations for the unknown angles α, β, and γ,

where 0 ≤ α ≤ 2π, 0 ≤ β ≤ 2π, 0 ≤ γ ≤ π.

2 sin α – cos β + 3 tan γ = 3

4 sin α + 2 cos β - 2 tan γ = 2

6 sin α – 3 cos β + tan γ = 9

6. The figure shows the graph of cubic of a cubic equation . Find

the coefficients a, b, c, and d.

(0,10) (1,7)

(4,-14)

(3,-11)

By: Fitria Khasanah page 3

EXERCISE 2 OF ELEMENTARY LINEAR ALGEBRA

(Get into groups of four or five persons)

Meeting-7

1. Find a row operation that will restore the given elementary matrix to an identity matrix.

a.

b.

2. Find the inverse of the given matrix if the matrix is invertible and check your answer by

multiplication.

a.

b.

3. Find the inverse of each of the following 4 x 4 matrices, where are

all nonzero

a.

b.

By: Fitria Khasanah page 4

4. Consider the matrix

A=

Find elementary matrices dan such that

5. Solve the general system by inverting the coefficient matrix

a.

b.

c.

6. Let A a square matrix.

a. Proof that

b. Proof that

By: Fitria Khasanah page 5

Kisi-Kisi Ujian Tengah Semester

1. Penyelesaian SPL dengan Metode Eliminasi Gauss

2. Penyelesaian SPL dengan Metode Eliminasi Gauss-Jordan

3. Mencari invers dari suatu matriks

4. Menemukan matriks elementer

5. Pembuktian pada matriks kuadrat