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Home Assignment 1.1. DETERMINANTS
(Translate and prepare yourself for the test)
In Problems 1– 6 calculate the given determinants
Pr 1. ; Pr 2. ; Pr 3. ;
Pr 4. ; Pr 5. ; Pr 6. ;
Pr. 7. Find the values of the parameter x making the matrix A a singular one: ;
Pr. 8. Calculate the determinant expanding it into the sum: ;
Pr. 9. Prove without calculation that the determinant Δ is a multiple of 7: ;
Hint. Multiply the first column by 1000, and the second one by 100, and the third one by ten then add all the multiples to the fourth column. Notice that the numbers 4319, 3003, 2996 and 1015 are the multiples of 7.
Pr. 10. Calculate the determinant Δ of -st order:
Δ .
Hint. Subtract the first row from every rest and then add the every rest to the new first row.
The answers: Pr 1. –29; Pr 2. 119; Pr 3. 21; Pr 4. 0; Pr 5. 0; Pr 6. 1800; Pr 7. {1, –0.1};
Pr 8. 22(bc - ad); Pr 10. .
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