5. Suppose that [ operatorname{det}left[egin{array}{lll} a & b & c \ d & e & f \ g & h & i end{array} ight]=6 ] What is [ operatorname{det}left[egin{array}{ccc} b & e & -3 h \ a+3 c & d+3 f & -3 g-9 i \ c & f & -3 i end{array} ight] ] You should not calculate a formula for the determinant, instead use properties of the determinant and work out which operations you need to carry out to get from one matrix to the other.
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The determinant changes sign when two rows or columns are swapped, so swapping the first and second columns changes the determinant to -6. Multiplying a row or column by a scalar multiplies the determinant by that scalar, so multiplying the third column by -3 Show more…
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Suppose that $$A=\left[\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & i \end{array}\right] \text { and } \operatorname{det}(A)=4$$. Compute the determinant of each matrix below. $$\left[\begin{array}{ccc} a-5 d & b-5 e & c-5 f \\ 3 g & 3 h & 3 i \\ -d+3 g & -e+3 h & -f+3 i \end{array}\right]$$.
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Hi Please assist me with determinant matrix
Lien L.
Compute the following determinants: det([A]) = | -3 1 5 | | -3 4 2 | | -3 2 1 | det([B]) = | 1 2 3 | | 4 5 6 | | 7 8 9 | Compute det([A][B]) using properties of the determinant. Hint: this should be very quick to do. Do not compute the product of the matrices [A] and [B]!
Steven C.
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