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Practice: Determinant

Related Topics

Wize University Linear Algebra Textbook > Determinants

Determinants of Large Matrices

5 Activities

Wize University Linear Algebra Textbook > Determinants

(Optional) Shortcut for 3x3 Determinants

3 Activities

Practice: Determinant

Find the determinant of [40151002−2]\begin{bmatrix} 4&0&1\\ 5&1&0\\ 0&2&-2 \end{bmatrix}.

More Determinants of Large Matrices Questions:
133 - FML 3 - 18.1W e.g. 8
Find the determinant of the matrix A=  [102−321−21−101−10−21−1]\bcb{\boldsymbol{ A =  \begin{bmatrix} 1 & 0 & 2 & -3 \\ 2 & 1 & -2 & 1 \\ -1 & 0 & 1 & -1 \\ 0 & -2 & 1 & - 1\end{bmatrix} }}
133 - FML 3 - 18.1W e.g. 77
Find the determinant of the matrix A=[102−3021−210−101100−21−11001−10]\bcb{\boldsymbol{A = \begin{bmatrix} 1 & 0 & 2 & -3 & 0 \\ 2 & 1 & -2 & 1 & 0 \\ -1 & 0 & 1 & 1 & 0 \\ 0 & -2 & 1 & -1 & 1 \\ 0 & 0 & 1 & -1 & 0 \end{bmatrix} }}
Determinants of Large Matrices
Compute the determinant of A=[−214−110−125−121003−1]A=\left[\begin{array}{rrrr} -2&1&4&-1\\ 1&0&-1&2\\ 5&-1&2&1\\ 0&0&3&-1 \end{array}\right].
Determinants of Large Matrices
B=[40151002−2]B= \begin{bmatrix} 4&0&1\\ 5&1&0\\ 0&2&-2 \end{bmatrix}
Find det(B)\det B.
Determinants and Inverse
Let B=[1−102111000−11−21−2−1]B=\left[\begin{array}{rrrr} 1&-1&0&2\\ 1&1&1&0\\ 0&0&-1&1\\ -2&1&-2&-1 \end{array}\right], and note that det(B)=−1\text{det}(B)=-1.
Use the inverse formula to find the (4,3)(4,3)-entry of B−1B^{-1}.
Practice: Determinant
Practice Question: Determinant
Find the determinant of [40151002−2]\begin{bmatrix} 4&0&1\\ 5&1&0\\ 0&2&-2 \end{bmatrix}.
Cramer's Rule: Linear Systems
Let A=[−1−2430−215−1]A=\begin{bmatrix} -1&-2&4\\ 3&0&-2\\ 1&5&-1 \end{bmatrix}.
(a) Find detA\text{det}A.
(b) User Cramer's Rule to find the value of xx in the unique solution to Ax=bA\bm{x}=\bm{b}, where x=[xyz]\bm{x}=\begin{bmatrix} x\\y\\z \end{bmatrix} and b=[00−2]\bm{b}=\begin{bmatrix} 0\\0\\-2 \end{bmatrix}
Determinants and Inverses
Let A=[abcdef12−3]A=\begin{bmatrix} a&b&c\\ d&e&f\\ 1&2&-3 \end{bmatrix}, where it is known that det[abde]=5\text{det}\begin{bmatrix} a&b\\d&e \end{bmatrix}=5, det[acdf]=−2\text{det}\begin{bmatrix} a&c\\d&f \end{bmatrix}=-2 and det[bcef]=3\text{det}\begin{bmatrix} b&c\\e&f \end{bmatrix}=3.
(a) Find detA\text{det}A.
(b) Find the (2,3)-entry of AdjA\text{Adj}A.
Determinants of Large Matrices
Given A=[459093−20−1]A= \begin{bmatrix} 4&5&9\\ 0&9&3\\ -2&0&-1\\ \end{bmatrix},
a.) Find the (2, 1)-minor of A.
b.) Find the (1, 3)-cofactor of A.
Determinants of Large Matrices
Compute the determinant of B=[021−4−1321001−2−1322]B= \begin{bmatrix} 0&2&1&-4\\ -1&3&2&1\\ 0&0&1&-2\\ -1&3&2&2 \end{bmatrix} .
More (Optional) Shortcut for 3x3 Determinants Questions:
133 - FML 3 - 18.1W e.g. 71
  ⁣B‾=  [1234−112x2]\bcb{\boldsymbol{ \ul{B} =  \begin{bmatrix} 1 & 2 & 3 \\ 4 & -1 & 1 \\ 2 & x & 2 \end{bmatrix} }} such that det(  ⁣B‾)=−8 \bcb{\boldsymbol{ \det {\ul{B}} = -8 }} , then x\bcb{\boldsymbol{ x }} is:
(a)  111(b)  −1(c)  0(d)  None of the above\text{(a)}\;\boldsymbol{ \frac{1}{11} } \qquad\qquad\qquad \text{(b)}\; \boldsymbol{ -1}\qquad\qquad\qquad \text{(c)}\; \boldsymbol{ 0}\qquad\qquad\qquad \text{(d)}\; \text{\bf{None of the above}}
Shortcut for 3x3 Determinants
Let A=[−61aa−2001−2]A=\left[\begin{array}{rrr} -6&1& a\\ a&-2&0\\ 0&1& -2 \end{array}\right]. Find the value(s) of aa such that AA is not invertible.
Determinants of Large Matrices
B=[40151002−2]B= \begin{bmatrix} 4&0&1\\ 5&1&0\\ 0&2&-2 \end{bmatrix}
Find det(B)\det B.
Practice: Determinant of $3\times3$ Matrix
Let A=[61aa−20012]A=\left[\begin{array}{rrr} 6&1&a\\ a&-2&0\\ 0&1&2 \end{array}\right] using cofactor expansion along any row or column
Find the value(s) of aa that will make AA invertible
Practice: Determinant
Practice Question: Determinant
Find the determinant of [40151002−2]\begin{bmatrix} 4&0&1\\ 5&1&0\\ 0&2&-2 \end{bmatrix}.