Question

the rank of the zero matrix of order 3 ×4 is​

Answer 1

Answer:

What is the rank of a zero matrix?

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Once you put your matrix in echelon form using the elementary operations of swapping rows, and adding multiples of rows to another the rank is how many rows that are nonzero.

The zero matrix is already in echelon form and all of the rows are all zeros. The rank is then zero.

In fact the only matrix with rank zero is the zero matrix.

Can rank of a matrix be 0?

What is the rank of a matrix?

What's the rank of a matrix?

What is the rank of a matrix?

How can I find the rank of a matrix?

The rank of zero matrix is zero.

The rank denotes how many linearly independent vectors are held in the matrix. The row reduced matrix illustrates this by simplification.

How many vectors are in a zero matrix?

None, no vectors at all, not even linearly independent vectors.

So that is a rank of zero.

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Zero.

The rank is the max number of linear independent row vectors (or what amounts to the same, linear independent column vectors.

For a zero matrix the is just the zero vector, hence rank equals zero.

The zero matrix represents the linear transformation sending all vectors to the zero vector. The zero matrix is idempotent, meaning that when it is multiplied by itself the result is itself. The zero matrix is the only matrix whose rank is 0.

What is the meaning of low rank matrix?

What is a non zero minor of largest order determine the rank of matrix?

What is an intuitive explanation of the rank of a matrix?

What is the order of zero matrix?

How do I write a 3x3 matrix A that has rank 2 (rank(A) = 2)?

The rank of a matrix equals the number of linearly independent rows which also equals the number of linearly independent columns. Only the zero matrix has rank zero.

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The rank of a zero matrix is always zero. Because all elements(diagonal and off diagonal elements) of a zero matrix are zero.

So a zero matrix is always in the echelon form due to which it’s rank is always zero.