Let A,B be two matrices with linearly independent columns . If Col(A)=Col(B) then A(A^TA)^{-1}A^T=B(B^TB)^{-1}B^T True or False?

Question

Question

Answers (1)

Relevant Questions

asked 2021-01-31

Let A,B and C be square matrices such that AB=AC , If \(A \neq 0\) , then B=C.
Is this True or False?Explain the reasosing behind the answer.

See answers (1)

asked 2020-11-10

If \(A=\begin{bmatrix}-2 & 1&-4 \\-2 & 4&-1 \\ 1 &-1 &-4 \end{bmatrix} \text{ and } B=\begin{bmatrix}-2 & 4&2 \\-4 & -1&1 \\ 4 &1 &1 \end{bmatrix}\)
then AB=?
BA=?
True or false : AB=BA for any two square matrices A and B of the same size.

See answers (1)

asked 2021-01-04

In the following question there are statements which are TRUE and statements which are FALSE.
Choose all the statements which are FALSE.
1. If the number of equations in a linear system exceeds the number of unknowns, then the system must be inconsistent - thus no solution.
2. If B has a column with zeros, then AB will also have a column with zeros, if this product is defined.
3. If AB + BA is defined, then A and B are square matrices of the same size/dimension/order.
4. Suppose A is an n x n matrix and assume A^2 = O, where O is the zero matrix. Then A = O.
5. If A and B are n x n matrices such that AB = I, then BA = I, where I is the identity matrix.

See answers (1)

asked 2021-01-16

Let W be the vector space of \(3 \times 3\) symmetric matrices , \(A \in W\) Then , which of the following is true ?
a) \(A^T=1\)
b) \(dimW=6\)
c) \(A^{-1}=A\)
d) \(A^{-1}=A^T\)

See answers (1)

asked 2021-03-06

Let A and B be Hermitian matrices. Answer true or false for each of the statements that follow. In each case, explain or prove your answer. The eigenvalues of AB are all real.

See answers (1)

asked 2021-01-13

Mark each of the following statement true or false: If A and B are matrices such that AB = O and \(A \neq O\), then B = O.

See answers (1)

asked 2020-12-29

If A and B are \(n \times n\) diagonalizable matrices , then A+B is also diagonalizable.
True or False?

See answers (1)

asked 2020-11-30

True or False
If A and B are \(n \times n\) lower triangular matrices, then AB is also lower triangular

See answers (1)

asked 2020-12-03

If A and B are both \(n \times n\) matrices (of the same size), then
det(A+B)=det(A)+det(B)
True or False?

See answers (1)

asked 2021-02-19

Determine whether each of the following statements is true or false, and explain why.If A and B are square matrices of the same size, then AB = BA

See answers (1)

Answer 1

Step 1
Let A and B are two matrices.
And A and B are linearly independent columns.
Step 2
If col(A) =col(B)
Since A and B are linearly independent.
So \(\alphaA +\betaB =0\)
So, the matrices are orthonormal,
So \(AA^T =BB^T\)
From this,
\((AA^T)^{-1} =(BB^T)^{-1}\)
Then,
\(A(A^TA)^{-1}A^T=B(B^TB)^{-1}B^T\)
Since in matrices,
AA^T= \neq A^TA
So the answer is false.
The correct option is (2).

Didn’t find what you are looking for?

Let A,B be two matrices with linearly independent columns . If Col(A)=Col(B) then A(A^TA)^{-1}A^T=B(B^TB)^{-1}B^T True or False?

Answers (1)

Relevant Questions