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Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 3 0 -4 2 0 6 -3 0 8
a. The matrix is invertible. The columns of the given matrix span R^3.
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
c. The matrix is invertible. The given matrix has 2 pivot positions.
d. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution.

Answer :

gkosworldreign

Answer:

b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

Step-by-step explanation:

A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.

3  0 -4

2  0  6

-3 0  8

 

Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )

MrRoyal

A square matrix is said to be invertible if it has an inverse.

The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

The matrix is given as:

[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]

Calculate the determinant

The determinant of the matrix calculate as:

[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]

[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]

[tex]|A| = 0 - 0 -0[/tex]

[tex]|A| = 0[/tex]

When a matrix has its determinant to be 0, then

  • It is not invertible
  • It does not form a linear independent set.

Hence, the correct option is (b)

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