# Invertible Matrix: Find Values of p & q

• magnifik
In summary, the matrix is a 3x3 matrix with the values 0, 1, b, -1, 0, c, and -b, -c, 0. The determinant is found to be 0 for all values of b and c, leading to the conclusion that the matrix is singular and not invertible. Therefore, there are no values of b and c for which the matrix is invertible.
magnifik
for what values of p and q is this matrix invertible?

this is all one 3x3 matrix. sorry for ugly formatting.
[0 1 b]
|-1 0 c|
[-b -c 0]

i found the determinant to be 0 + (-bc) + bc - 0 - 0 - 0 = -bc + bc = 0
so i came the conclusion that the matrix is singular or not invertible. is this correct, or am i missing something?

magnifik said:
i found the determinant to be 0 + (-bc) + bc - 0 - 0 - 0 = -bc + bc = 0
so i came the conclusion that the matrix is singular or not invertible. is this correct, or am i missing something?
This sounds correct. So for what values of b and c is the matrix invertible?

since it isn't invertible, i suppose there are no values for which b and c are invertible

That sounds right.

## 1. What is an invertible matrix?

An invertible matrix is a square matrix that has an inverse matrix, meaning it can be multiplied by another matrix to result in the identity matrix (a matrix with 1s on the main diagonal and 0s everywhere else).

## 2. How do you determine if a matrix is invertible?

A matrix is invertible if its determinant (the value obtained by performing a specific calculation on the matrix) is not equal to zero.

## 3. Can all matrices be inverted?

No, only square matrices (matrices with the same number of rows and columns) can be inverted. Additionally, a matrix must have a non-zero determinant to be invertible.

## 4. What are the steps to find the values of p and q in an invertible matrix?

The values of p and q can be found by setting up an equation using the given information and the properties of an invertible matrix. The equation can be solved using algebraic manipulation and solving for the variables.

## 5. Are there any special properties of invertible matrices?

Yes, invertible matrices have several important properties, such as having a unique inverse, being able to be multiplied by another invertible matrix to result in another invertible matrix, and preserving linear independence and linear combinations of vectors.

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