if u is a square matrix such that u tu = i, what can we say about det(u)? explain, of course

What is a square matrix determinant?

Definition of Determinant of Matrix. The determinant of a matrix is the scalar value or number calculated using a square matrix. The square matrix could be 2×2, 3×3, 4×4, or any type, such as n × n, where the number of column and rows are equal.

Why do only square matrices have determinants?

Answer: The determinant of a matrix is a scalar property of that matrix, which can be thought of physically as the volume enclosed by the row vectors of the matrix. Only square matrices have determinants. Determinants are also useful because they tell us whether or not a matrix can be inverted.

Are determinants only for square matrices?

Properties of Determinants The determinant is a real number, it is not a matrix. The determinant can be a negative number. It is not associated with absolute value at all except that they both use vertical lines. The determinant only exists for square matrices (2×2, 3×3, ... n×n).

How do you know if a matrix is a square matrix?

Calculate the number of rows and columns present in the array and store it in variables rows and columns respectively. Initialize variable flag to true. Check if given matrix has the same number of rows and columns(square matrix). If not, print the error message "Matrix should be a square matrix."

How do you know if a matrix is a square?

If a matrix has the same number of rows and columns (e.g., if m == n), the matrix is square.

Why non square matrix has no determinant?

The determinant of a matrix is the product of its eigenvalues. Non-square matrices don't have eigenvalues, so you can't define determinants for them.

For which type of matrix we can find determinant?

square matrixFor a square matrix, i.e., a matrix with the same number of rows and columns, one can capture important information about the matrix in a just single number, called the determinant.

Is the determinant defined for non square matrix?

The determinant of any square matrix A is a scalar, denoted det(A). [Non-square matrices do not have determinants.]

Can you find determinant of 2x3 matrix?

Hence, It's not possible to find the determinant of a 2 × 3 matrix because it is not a square matrix.

What is the determinant of a non square matrix?

The determinant of any square matrix A is a scalar, denoted det(A). [Non-square matrices do not have determinants.]

Do only square matrices have inverses?

Inverses only exist for square matrices. That means if you don't the same number of equations as variables, then you can't use this method. Not every square matrix has an inverse.

Does inverse exist for non square matrix?

Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse.

What is the smallest subspace of V?

Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span {u, v}. this shows that Span {u, v} is the smallest subspace of V that contains both u and v.

What is the formula for det B?

c. If one row of A is multiplied by k to produce B, then det B = k * det A.

What is the null space of a matrix?

The null space of an m x n matrix A, written as Nul A, is the set of all solutions of the homogeneous equation Ax = 0.

What is vector space?

A vector space is a nonempty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars, subject to the ten axioms listed below.

Why is zero vector in H?

Zero vector is in H because 0 = 0v1 + 0v2.

What is the value of all polynomials of the form p (t)?

All polynomials of the form p (t) = at^2.

How to find the g in H?

1. Let g (t) = 0 for all t. Then g (a) = g (b) = 0, so g is in H .