BEFORE YOU POST YOUR WORK MAKE SURE YOU POST PICTURES OF YOUR WORK AND DO NOT TYPE IT, IT'S HARDER TO UNDERSTANDCan you please solve everything of what is asking on the picture by using the matrix provided. Make sure you explain each step you make and show all of your work.for the matrix just choose any matrix you want but it has to be a 3x3.Thank you **Initial Post Prompt**Select a square matrix (3 x 3 or larger) from anywhere in our textbook, outside of chapter 7. Call the matrix A and make sure you tell us what the matrix is.Then:1. Give all the eigen-information for the matrix A, including: 1. Characteristic Polynomial 2. Eigenvalues and eigenvectors 3. Algebraic multiplicity 4. Geometric multiplicity 5. Eigenspaces2. State whether or not we can use the eigenvectors of A to form an eigenbasis. If so, state the eigenbasis.3. State whether or not the matrix is defective or non-defective.4. State if the matrix is diagonalizable and state how you know.5. If the matrix is diagonalizable, then diagonalize the matrix.

As a question with multiple sub-parts and multiple questions were posted, we can solve first three sub-parts of the first question as per Bartleby guidelines. To get remaining sub-parts and questions solved please repost the complete question and mention the sub-parts to be solved. Instructions: Take any 3×3 matrix 1. Find the characteristic polynomial. 2. Eigen values and Eigen vectors. 3. Algebraic Multiplicity. Note: Characteristic polynomial can be determined by A-λI. Characteristic roots can be determined by solving A-λI=0. Characteristic vectors can be determined by AX=λX The algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic polynomial. Take 3×3 matrix are as follows: A=10002-2103 Find the characteristic equation: A-λI= 1-λ0002-λ-2103-λ= 1-λ2-λ3-λ= 2-λ-2λ+λ23-λ= 2-3λ+λ23-λ= 6-9λ+3λ2-2λ+3λ2-λ3=-λ3+6λ2-11λ+6 Hence, the characteristic polynomial is -λ3+6λ2-11λ+6. Find the eigen value: A-λI=01-λ2-λ3-λ=0λ=1,2,3 The eigen values for the given matrix are 1,2,3. Eigen vector: Ax=λx10002-2103x1x2x3=x1x2x300001-2102x1x2x3=000x1+2x3=0⇒x3=-12x1x2-2x3=0⇒x2=x1x1x2x3=11-12 Hence, the eigen vector corresponds to λ=1 is 11-12 as x1 as free variable. Eigen vector: Ax=λx10002-2103x1x2x3=2x12x22x3-10000-2101x1x2x3=000x1+x3=0-x1=0-2x3=0x1x2x3=010x2 Hence, the eigen vector corresponds to λ=2 is 010. Eigen vector: Ax=λx10002-2103x1x2x3=3x13x23x3-2000-1-2100x1x2x3=000-2x1=0x1=0-x2-2x3=0⇒-x2=2x3x1x2x3=0-21x3 Hence, the eigen vector corresponds to λ=3 is 0-20. As there are no roots repeated, algebraic multiplicity is one. Hence, the algebraic multiplicity of all the roots is one.