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Row Echelon Form

Let A be a 4 ...

Question

Let A be a 4 $\times$ 3 real matrix with rank 2. Which one of the following statement is TRUE?

Rank of

A^{T} A

is less than 2

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Rank of

A^{T} A

is equal to 2

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Rank of

A^{T} A

is greater than 2

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Rank of

A^{T} A

can be any number between 1 and 3

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Solution

The correct option is B Rank of $A^{T} A$ is equal to 2
From the property of the rank of matrix

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Similar questions

\times

\times

A^{T} A)^{- 1} A^{T}

M

3 \times 3

I

3 \times 3

M^{- 1} = adj (adj M),

2 \times 2

\to x

[x_{1}, x_{2}]^{T}

| | \to x | | = (X_{1}^{2} + X_{2}^{2})^{\frac{1}{2}}

3 \times 3

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