Question 5 - Week 4 Practice

00:00

26 Oct 2025

Q5.The trace of a square matrix

A

is defined as the sum of its diagonal entries. Consider the set

W

whose elements are

3\times 3

matrices with zero trace, i.e.

W=\left\{\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}\in M_{3\times3}(\mathbb{R})\mid a_{11}+a_{22}+a_{33}=0\right\}.

W

is a vector space with the standard operations of addition and scalar multiplication. Find the dimension of

W

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00:00

26 Oct 2025

Q5.The trace of a square matrix

A

is defined as the sum of its diagonal entries. Consider the set

W

whose elements are

3\times 3

matrices with zero trace, i.e.

W=\left\{\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}\in M_{3\times3}(\mathbb{R})\mid a_{11}+a_{22}+a_{33}=0\right\}.

W

is a vector space with the standard operations of addition and scalar multiplication. Find the dimension of

W

Your Answer

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00:00

26 Oct 2025

Q5.The trace of a square matrix

A

is defined as the sum of its diagonal entries. Consider the set

W

whose elements are

3\times 3

matrices with zero trace, i.e.

W=\left\{\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}\in M_{3\times3}(\mathbb{R})\mid a_{11}+a_{22}+a_{33}=0\right\}.

W

is a vector space with the standard operations of addition and scalar multiplication. Find the dimension of

W

Your Answer

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00:00

26 Oct 2025

Q5.The trace of a square matrix

A

is defined as the sum of its diagonal entries. Consider the set

W

whose elements are

3\times 3

matrices with zero trace, i.e.

W=\left\{\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}\in M_{3\times3}(\mathbb{R})\mid a_{11}+a_{22}+a_{33}=0\right\}.

W

is a vector space with the standard operations of addition and scalar multiplication. Find the dimension of

W

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